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# mikeross2694

Brent@GMATPrepNow posted a reply to The average salary of 15 people in the shipping department in the Problem Solving forum
“]The average salary of 15 people in the shipping department at a certain firm is $20,000 So, (sum of all 15 salaries)/15 =$20,000 Multiply both sides by 15 to get: sum of all 15 salaries = $300,000 The salary of 5 of the employees is$25,000 each and the salary of 4 of the employees is $16,000 ...” Today Brent@GMATPrepNow posted a reply to In how many different ways can 3 fiction books and 3 in the Problem Solving forum “Take the task of arranging the 6 books and break it into stages. Stage 1: Arrange the 3 fiction books in a row We can arrange n unique objects in n! ways So, we can arrange the 3 books in 3! ways (= 6 ways) So, we can complete stage 1 in 6 ways Stage 2: Arrange the 3 non-fiction books in ...” Today Brent@GMATPrepNow posted a reply to Data sufficiency in the GMAT Math forum “Take: y = 1 + 1/x Rewrite as: y = x/x + 1/x Simplify: y = (x + 1)/x So, we''re looking for an answer choice that can be expressed as a fraction in which the numerator is 1 greater than the denominator. Answer: E Cheers, Brent” Yesterday Brent@GMATPrepNow posted a reply to If is n is multiple of 5, and n=p^2*q where p and q are prim in the Problem Solving forum “Let''s test some values that satisfy the given conditions (n is multiple of 5, and n = p²q, where p and q are prime numbers) How about: p = 2 and q = 5. In this case, n = (2²)(5) = 20, and 20 is a multiple of 5, which satisfies the given condition. Now plug p = 2 and q = 5 into the ...” Yesterday Brent@GMATPrepNow posted a new topic called If 3 different integers are randomly selected from the set { in the Problem Solving forum “If 3 different integers are randomly selected from the set {1, 2, 3, 4, 5, 6}, what is the probability that a triangle can be constructed so that its 3 sides have the lengths of the 3 selected numbers? A) 0.25 B) 0.3 C) 0.35 D) 0.40 E) 0.45 Source: www.gmatprepnow.com Difficulty level: ...” Yesterday Brent@GMATPrepNow posted a reply to A certain zoo has mammal and reptiles and birds, and no in the Data Sufficiency forum “Target question: How many birds are in the zoo? Given: The ratio of mammals to reptiles to birds is 11: 8:5. Given this ratio, we could say that there are: 11x mammals 8x reptiles 5x birds for some value of x. Statement 1: there are twelve more mammals in the zoo than there are ...” Yesterday Brent@GMATPrepNow posted a reply to If x, y and z are three different non-negative integers, whi in the Problem Solving forum “Nice work, Mitch! I created this question to illustrate the importance of checking the answer choices each time you analyze one of the statements. Here’s why: Once we know that statement i COULD be true (it''s true when x = 0, y = 1 and z = 2), we should check the answer choices…. ...” June 18, 2019 Brent@GMATPrepNow posted a reply to A certain machine produces 1,000 units of product P per hour in the Problem Solving forum “A certain machine produces 1,000 units in 1 hour So, the machine produces 24,000 units in 24 hours In other words, the machine produces 24,000 units in 1 DAY So, the machine produces (24,000)(7) units in 7 DAYS (20,000)(7) = 140,000 So, (24,000)(7) = some number greater than 140,000 ...” June 18, 2019 Brent@GMATPrepNow posted a new topic called If x, y and z are three different non-negative integers, whi in the Problem Solving forum “If x, y and z are three different non-negative integers, which of the following COULD be true? i) |x−y| = |x+y| = |y−z| ii) x^y = y^z iii) x³ + y³ = z³ A) i only B) ii only C) iii only D) i and ii E) i and iii Source; www.gmatprepnow.com Difficulty level: 700+ Answer: D” June 18, 2019 Brent@GMATPrepNow posted a reply to If p is an integer greater than 1, is p a prime number? in the Data Sufficiency forum “ Given: p is an integer greater than 1 Target question: Is p a prime number? Statement 1: p is a factor of 13 13 has exactly two factors: 1 and 13 Since p > 1, we KNOW that p = 13 (which is prime) The answer to the target question is YES, p IS prime Since we can answer the target ...” June 17, 2019 Brent@GMATPrepNow posted a reply to How many ways are there to arrange the letters in the word in the Problem Solving forum “------------ASIDE----------------- When we want to arrange a group of items in which some of the items are identical, we can use something called the MISSISSIPPI rule. It goes like this: If there are n objects where A of them are alike, another B of them are alike, another C of them are alike, ...” June 17, 2019 Brent@GMATPrepNow posted a reply to If |2x + 5| = |3x − 2|, which of the following is a possib in the Problem Solving forum “If |x| = |y|, then either x = y OR x = -y GIVEN: |2x + 5| = |3x − 2| So, EITHER 2x + 5 = 3x − 2 OR 2x + 5 = -(3x − 2) Let''s solve each equation... Take: 2x + 5 = 3x − 2 We get: 5 = x - 2 Solve: x = 7 Check answer choices.....x = 7 is not there. Try the other equation: Take: ...” June 17, 2019 Brent@GMATPrepNow posted a reply to Is h^2 = h? in the Data Sufficiency forum “Target question: Is h² = h? Statement 1: h + h = h Subtract h from both sides to get: h = 0 If h = 0, then h² = h becomes 0² = 0 (WORKS!) The answer to the target question is YES, h² = h Since we can answer the target question with certainty, statement 1 is SUFFICIENT Statement 2: ...” June 17, 2019 Brent@GMATPrepNow posted a reply to Is z > 0.5? in the Data Sufficiency forum “Target question: Is z > 0.5 ? SCAN the statements to see we can jump straight to.... Statements 1 and 2 combined There are infinitely-many values of z that satisfy BOTH statements. . Here are two: Case a: z = 0.6. In this case, the answer to the target question is YES, z IS greater ...” June 17, 2019 Brent@GMATPrepNow posted a reply to What is the value of x? in the Data Sufficiency forum “Target question: What is the value of x? Statement 1: 5x + 3y = 15 Since this is a linear equation with infinitely many solutions. Here are two: Case a: x = 3 and y = 0. In this case, the answer to the target question is x = 3 Case b: x = 0 and y = 5. In this case, the answer to the target ...” June 17, 2019 Brent@GMATPrepNow posted a reply to If the average (arithmetic mean) of seven consecutive in the Problem Solving forum “Another approach: For any set of consecutive integers, mean = median. So, in this case, mean = median = k + 2 So, the three values that come AFTER k + 2 are k+3, k+4, and k+5 And the three values that come BEFORE k + 2 are k-1, k, k+1, k+2, k+3, k+4, k+5 The product of the greatest and ...” June 17, 2019 Brent@GMATPrepNow posted a reply to Of the first three dozen cookies baked at a bake shop on a in the Data Sufficiency forum “ Given: Of the first three dozen (36) cookies baked at a bake shop on a certain day, 1/3 were chocolate chip cookies. 1/2 of the remaining cookies that were baked that day were chocolate chip cookies, 1/3 of 36 = 12. So, 12 chocolate cookies were baked in the first round of baking. Let x = ...” June 15, 2019 Brent@GMATPrepNow posted a reply to List $$K$$ consists of seven numbers. Is the average in the Data Sufficiency forum “Target question: Is the average (arithmetic mean) of the seven numbers negative? Statement 1: Four of the seven numbers in list K are negative. There are several scenarios that satisfy statement 1. Here are two: Case a: List K = {-10, -10, -10, -10, 1, 1, 1}. Average = sum/7 = -37/7. The ...” June 15, 2019 Brent@GMATPrepNow posted a reply to A set of 15 different integers has median of 25 and a range in the Problem Solving forum “Let''s tackle this one step at a time. First, we have 15 different integers. We can let these 15 spaces represent the 15 numbers written in ascending order: _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ If the median is 25, we can add this as the middle value: _ _ _ _ _ _ _ 25 _ _ _ _ _ _ _ Notice that 7 ...” June 15, 2019 Brent@GMATPrepNow posted a reply to 8, 5, x, 6 The median of the list of positive integers in the Problem Solving forum “Since there is an even number of values in the list, the median will be the AVERAGE of the two middlemost values (when all values are listed in ASCENDING order) Let''s the answer choices... A) If x = 3, then the values are {3, 5, 6, 8}, which means the median = (5 + 6)/2 = 5.5 NO GOOD. We ...” June 14, 2019 Brent@GMATPrepNow posted a reply to Will the first 10 volumes of a 20-volume encyclopedia fit in the Data Sufficiency forum “Target question: Will the first 10 volumes of a 20-volume encyclopedia fit upright in the bookrack shown above? Statement 1: x = 50 centimeters. We have no idea how THICK the first 10 volumes are. They COULD each be 1 mm thick, in which case the 10 volumes will easily fit in the 50 cm ...” June 14, 2019 Brent@GMATPrepNow posted a reply to For every integer $$k$$ from 1 to 10, inclusive the "k& in the Problem Solving forum “T = 1/2 - 1/4 + 1/8 - 1/16 + . . . Notice that we can rewrite this as T = (1/2 - 1/4) + (1/8 - 1/16) + . . . When you start simplifying each part in brackets, you''ll see a pattern emerge. We get... T = 1/4 + 1/16 + 1/64 + 1/256 + 1/1024 Now examine the last 4 terms: 1/16 + 1/64 + 1/256 + ...” June 14, 2019 Brent@GMATPrepNow posted a reply to Jim is twice as old as Fred ... in the Problem Solving forum “I''ve added the answer choices.... TODAY''S AGES Today Jim is twice as old as Fred, and Sam is 2 years younger than Fred. Let x = Fred''s age TODAY So, 2x = Jim''s age TODAY And x - 2 = Sam''s age TODAY AGES FOUR YEARS AGO Let''s first determine Jim''s age and Sam''s age FOUR YEARS ...” June 13, 2019 Brent@GMATPrepNow posted a reply to in terms of k and m in the Problem Solving forum “One approach is to plug in values. Let$100 be the original price per share of Stock X Choose a "nice" value for k. How about k = 200 So, after a 200% increase, the new price per share = $300 Let$100 be the original earnings per share of Stock X Choose a "nice" ...”
June 13, 2019
Brent@GMATPrepNow posted a reply to cd? in the Data Sufficiency forum
“Target question: Is the product cd positive? Statement 1: 3c = -8d³ Divide both sides by d to get: 3c/d = -8d² Divide both sides by 3 to get: c/d = -8d²/3 Rewrite as: c/d = (-8/3)(d²) Since d² is greater than or equal to zero for all values of d, and since -8/3 is NEGATIVE, we can ...”
June 13, 2019
Brent@GMATPrepNow posted a reply to If f(x) = x^3 + 9, is f(x) positive? in the Data Sufficiency forum
“ Given: f(x) = x³ + 9 Target question: Is f(x) positive? Statement 1: x < −1 Let''s TEST some values. There are several values of x that satisfy statement 1. Here are two: Case a: x = -2. In this case, f(-2) = (-2)³ + 9 = (-8) + 9 = 1. So, the answer to the target question is ...”
June 13, 2019
Brent@GMATPrepNow posted a reply to In May Mrs Lee's earnings were 60 percent of the Lee family' in the Problem Solving forum
“Since we''re asked to find a PERCENT (and not an actual value), we can assign a nice value to the Lee family''s total income. In May Mrs Lee''s earnings were 60 percent of the Lee family''s total income Let''s say $100 = Lee family''s total income IN MAY This means$60 = Mrs Lee''s earnings ...”
June 13, 2019
Brent@GMATPrepNow posted a reply to Which of the following could be the median for a set of in the Problem Solving forum
“Since 20 < x < 80, we can see that, if we arrange the 5 numbers in ASCENDING order, we get two possible cases: case a: {x, 56, 86, 97, 98} case b: {56, x, 86, 97, 98} In both cases, the median is 86 Answer: B Cheers, Brent”
June 13, 2019
Brent@GMATPrepNow posted a reply to a, b and c are three distinct integers, greater than 1, such in the Problem Solving forum
“150 = (2)(3)(5)(5) There are three sets of 3 values (each greater than 1) that have a product of 150: {2, 3, 25} {3, 5, 50} {2, 5, 15} GIVEN: The greatest common divisor of any two numbers, among the three integers, is 1 The only set that meets this condition is {2, 3, 25} SUM = 2 + 3 + ...”
June 12, 2019
Brent@GMATPrepNow posted a reply to David drove to work at an average (arithmetic mean) speed of in the Problem Solving forum
“Let''s start with a "word equation" We can write: (David''s travel time TO work) + (David''s travel time FROM work) = 2 hours time = distance/speed Let d = the distance each way We can write: d/45 + d/60 = 2 To eliminate the fractions, multiply both sides by 180, the LCM of 45 ...”
June 12, 2019
Brent@GMATPrepNow posted a reply to If x and y are positive integers, are x and y consecutive? in the Data Sufficiency forum
“ Given: x and y are positive integers Target question: Are x and y consecutive? Statement 1: x+y=3 Since x+y=3 are x positive integers, we know that one number must be 1 and the other number must be 2. The answer to the target question is YES, x and y ARE consecutive Since we can ...”
June 12, 2019
Brent@GMATPrepNow posted a reply to How many integers between in the Problem Solving forum
“We want to determine how many integers end in 13 For example, 324713, 324813, 324913, 325013, . . . etc. Recognize that, for every 100 consecutive integers, only 1 will end in 13. There are 133,900 integers between 324,700 and 458,600 (since 458,600 - 324,700 = 133,900) Of those 133,900 ...”
June 11, 2019
Brent@GMATPrepNow posted a reply to sum of these 24 integers? in the Problem Solving forum
“Since we''re adding 24 numbers, we know that: Six numbers will be in the form 1--- Six numbers will be in the form 2--- Six numbers will be in the form 3--- Six numbers will be in the form 4--- Let''s first see what the sum is when we say all 24 numbers are 1000, 2000, 3000 or 4000 The sum = ...”
June 11, 2019
June 11, 2019
Brent@GMATPrepNow posted a reply to A certain library in the Problem Solving forum
“1st day - $0.10 2nd day -$0.20 or $0.40 (double or add$0.30) $0.20 is the lesser amount 3rd day -$0.40 or $0.50 (double or add$0.30) $0.40 is the lesser amount 4th day -$0.80 or $0.70 (double or add$0.30) $0.70 is the lesser amount The correct answer is B Cheers, Brent” June 11, 2019 Brent@GMATPrepNow posted a reply to rates in the Problem Solving forum “Let''s assign a nice value to x (a value that will work well with all of the numbers 3, 4 and 6. Let''s say x = 24 GIVEN: 4 machines make x units in 6 days This means 4 machines make 24 units in 6 days So, 4 machines make 4 units in 1 day So, 1 machine makes 1 unit in 1 day From here, ...” June 11, 2019 Brent@GMATPrepNow posted a reply to DS in the Data Sufficiency forum “Target question: Is b (the y-coordinate of the point on the line) positive? Given: Line k passes through the origin and through the point (a,b) Statement 1: The slope of line k is negative There are several lines and points that satisfy statement 1. Here are two: Case a: ...” June 11, 2019 Brent@GMATPrepNow posted a reply to In a certain pond in the Problem Solving forum “We can use equivalent ratios here. We''re told that the proportion of tagged fish in the 50-fish SAMPLE is equal to the the proportion of tagged fish in the ENTIRE pond. So, (# tagged fish in SAMPLE)/50 = (total # tagged fish)/(total # of fish in POND) Let x = # of fish in the entire ...” June 11, 2019 Brent@GMATPrepNow posted a reply to In the multiplication above, # represents a single digit. in the Problem Solving forum “We''re told that # times 512 equals two thousand and something. Well, 4 times 512 = two thousand and something. And 5 times 512 = two thousand and something. No other digits, when multiplied by 512 will give us two thousand and something So, let''s test 4 and 5 (answer choices C and D) If ...” June 10, 2019 Brent@GMATPrepNow posted a reply to In the xy-plane shown, is the slope of the line L negative ? in the Data Sufficiency forum “Target question: Is the slope of the line L negative ? After scanning the two statement, I see that we can jump straight to . . . Statements 1 and 2 combined The COMBINED statements tell us that line l passes through quadrants III and IV. There are several lines that satisfy BOTH ...” June 10, 2019 Brent@GMATPrepNow posted a reply to If x ≠ −2, then 5x+10x+2=5x+10x+2 in the Problem Solving forum “Approach #2: We''re asked to evaluate (find the value of) the given expression. Since all of the answer choices are constants (just numbers), we know that the given expression must evaluate to be ONE of the answer choices FOR ALL VALUES OF X. So, let''s test a value of x Try x = 1 We get: ...” June 10, 2019 Brent@GMATPrepNow posted a reply to If x ≠ −2, then 5x+10x+2=5x+10x+2 in the Problem Solving forum “(5x+10)/(x+2) = (5(x+2))/(x+2) = 5 Answer: D Cheers, Brent” June 10, 2019 Brent@GMATPrepNow posted a reply to For any integers a and b, min(a, b) and max(a, b) denote in the Data Sufficiency forum “Notice that min(3, 4) = 3 Notice that min(2, 2) = 2 Notice that min(1, 11) = 1 KEY PROPERTY: In general, we can say that, if min(a,b) = c, then we know that c ≤ a and c ≤ b Target question: What is max(y, 8)? Statement 1: min(9, x) = y This tells us that y ≤ 9 Let''s test ...” June 10, 2019 Brent@GMATPrepNow posted a reply to From a group of 10 students, 7 girls and 3 boys, a teacher in the Problem Solving forum “Take the task of arranging students and break it into stages. Stage 1: Select two girls Since the order in which we select the women does not matter, we can use combinations. We can select 2 girls from 7 girls in 11C2 ways (21 ways) So, we can complete stage 1 in 21 ways If anyone is ...” June 10, 2019 Brent@GMATPrepNow posted a reply to If 3 different integers are randomly selected from the integ in the Problem Solving forum “I specifically created this question to illustrate the importance of calculating the denominator first (when using counting techniques to solve a probability question) There are two reasons why you should calculate the denominator first: 1) The denominator is almost always easier to calculate ...” June 7, 2019 Brent@GMATPrepNow posted a reply to Puzzling probability question in the Problem Solving forum “P(selecting a sibling pair) = P(select a business student with a sibling AND select a law student who is that business student''s sibling) = P(select a business student with a sibling) x P(select a law student who is that business student''s sibling) = 30/500 x 1/800 = 30/400,000 = 3/40,000 = ...” June 6, 2019 Brent@GMATPrepNow posted a new topic called If 3 different integers are randomly selected from the integ in the Problem Solving forum “If 3 different integers are randomly selected from the integers from 1 to 12 inclusive, what is the probability that a triangle can be constructed so that its 3 sides are the lengths of the 3 selected numbers? A) 3/8 B) 7/18 C) 19/44 D) 39/88 E) 11/24 Answer: C Source: ...” June 6, 2019 Brent@GMATPrepNow posted a reply to GMAT Prep in the Problem Solving forum “In the 4 months leading up to March, the company PRODUCES 4x rakes (4 months at x/month = 4x) On March 1, x/2 rakes are SHIPPED, leaving 3.5x rakes for which the company must pay storage fees. On April 1, x/2 rakes are SHIPPED, leaving 3x rakes for which the company must pay storage fees. ...” June 5, 2019 Brent@GMATPrepNow posted a reply to VIC question -- picking numbers in the Problem Solving forum “Originally, T people were to pay total cost of x dollars. So, each person pays x/T each. After S people drop out, there are T-S people to pay total cost of x dollars. So, each person pays x/(T-S) each. The additional amount that each must pay = New cost per person - original cost per ...” June 5, 2019 Brent@GMATPrepNow posted a reply to Hotel California in the Problem Solving forum “One option is to use the Double Matrix method. Here, we have a population of lightbulbs, and the two characteristics of each bulb are: - incandescent or fluorescent - on or off Since the questions asks us to find a certain PERCENT, let''s say that there are 100 bulbs altogether. So, we ...” June 5, 2019 Brent@GMATPrepNow posted a reply to Of the 12 temporary employees in a certain company, 4 will in the Problem Solving forum “Take the task of selecting the employees and break it into stages. Stage 1: Select the 3 women The order in which we select the women does not matter, so we can use combinations. We can select 3 women from 5 women in 5C3 ways (= 10 ways) Aside: If anyone is interested, here''s video on ...” June 5, 2019 Brent@GMATPrepNow posted a reply to If k is 96% greater than its reciprocal, which of the follow in the Problem Solving forum “k is 96% greater than its reciprocal The reciprocal of k is 1/k So, we can write: k = (1/k) + (96% of 1/k) In other words: k = (1/k) + 0.96(1/k) Simplify: k = 1.96(1/k) Simplify: k = 1.96/k Multiply both sides by k to get: k² = 1.96 Solve: k = 1.4 of k = -1.4 Rewrite as follows: k = 7/5 of ...” June 5, 2019 Brent@GMATPrepNow posted a new topic called If k is 96% greater than its reciprocal, which of the follow in the Problem Solving forum “If k is 96% greater than its reciprocal, which of the following is an integer? A) 3k/7 B) 3k/5 C) 5k/7 D) 5k/3 E) 7k/5 Source: www.gmatprepnow.com Difficulty level: 600-650 Answer: C” June 4, 2019 Brent@GMATPrepNow posted a reply to Which of the following sets contains only factors of 45? in the Problem Solving forum “Scan the answer choices....(C and D)..... 13 is NOT a factor of 45. ELIMINATE C By the process of elimination, the correct answer is D Cheers, Brent Scan the two remaining answer choices.... 7 is NOT a factor of 45. ELIMINATE A, B and E” June 3, 2019 Brent@GMATPrepNow posted a reply to A company has two types of machines, type R and type S. in the Problem Solving forum “Here''s another approach . . . When it comes to questions where we must complete an entire job, I often (not always) like to know what can be accomplished in 1 unit of time (in this case, 1 hour). Machine R can complete 1/36 of the job in 1 hour. Machine S can complete 1/18 of the job in 1 ...” June 3, 2019 Brent@GMATPrepNow posted a reply to A company has two types of machines, type R and type S. in the Problem Solving forum “One approach is to assign a "nice" value to the job. Say, the job is to make 36 widgets. R does a certain job in 36 hours This means that machine R''s rate is 1 widget/hour S does the job in 18 hours This means that machine S''s rate is 2 widgets/hour So, their combined rate ...” June 3, 2019 Brent@GMATPrepNow posted a reply to If k^2 = m^2, which of the following must be true? in the Problem Solving forum “The question asks us what MUST be true. So, if we can find a case where a statement is not true, we can eliminate that answer choice. So, for example, one solution to the equation (k² = m²) is k = 1 and m = 1 Now let''s check the answer choices. A. k = m. Test: 1 = 1. Works. Keep A. B. ...” June 3, 2019 Brent@GMATPrepNow posted a reply to A company that ships boxes to a total of 12 distribution in the Problem Solving forum “We need to be able to create AT LEAST 12 codes (to represent the 12 countries). Let''s test the options. Can we get 12 or more color codes with 4 colors? Let''s see . . . 1-color codes = 4 (since there are 4 colors) 2-color codes = We need to choose 2 colors from 4. This can be ...” June 2, 2019 Brent@GMATPrepNow posted a reply to What is the total cost to make 7 long distance telephone in the Data Sufficiency forum “When we SCAN the statements, we see the key phrase: at least This allows us to jump straight to... Statements 1 and 2 combined There are infinitely many scenarios that satisfy BOTH statements. Here are two: Case a: Each call was 2 minutes long, for a total of 14 minutes. At$0.32 per ...”
June 1, 2019
Brent@GMATPrepNow posted a reply to Of the 60 animals on a certain farm, $$\frac{2}{3}$$ are in the Data Sufficiency forum
“Target question: How many of the animals are cows? Given: Of the 60 animals in a certain farm, 2/3 are either pigs or cows Let P = # of pigs Let C = # of cows 2/3 of 60 = 40, so we can say that P + C = 40 Statement 1: The farm has MORE THAN twice as many cows as it has pigs. In other ...”
May 31, 2019
Brent@GMATPrepNow posted a reply to A computer programmer needs to print 148 documents. The in the Problem Solving forum
“We can also answer this question using a step-by-step approach based on number sense. IMPORTANT: The word approximately typically suggests that we can be somewhat aggressive with our estimation There are 148 documents and the documents have an average length of 10 pages So, the TOTAL number ...”
May 29, 2019
Brent@GMATPrepNow posted a reply to x + 2y + 3z = 4 and 5x + 4y + 3z = 8. What is the value of x in the Problem Solving forum
“GIVEN: x + 2y + 3z = 4 5x + 4y + 3z = 8 ADD the two equations to get: 6x + 6y + 6z = 12 Factor: 6(x + y + z) = 12 Divide both sides by 6 to get: x + y + z = 2 Answer: B Cheers, Brent”
May 28, 2019
Brent@GMATPrepNow posted a reply to Two different primes may be said to"rhyme" around in the Problem Solving forum
“If two numbers are rhyming primes, then the integer the rhyme around will be the AVERAGE of the two primes. For example, 3 and 7 rhyme around 5. Notice that the AVERAGE of 3 and 7 is 5. Likewise, 5 and 23 rhyme around 14, and the AVERAGE of 5 and 23 is 14. Now onto the solution... List ...”
May 28, 2019
Brent@GMATPrepNow posted a reply to A certain fruit stand sold apples for $0.70 each and bananas in the Problem Solving forum “Here''s an approach where we test the POSSIBLE SCENARIOS. FACT #1: (total cost of apples) + (total cost of bananas) = 630 CENTS FACT #2: total cost of bananas is DIVISIBLE by 50, since each banana costs 50 cents. Now let''s start testing POSSIBLE scenarios. Customer buys 1 apple. 1 ...” May 28, 2019 Brent@GMATPrepNow posted a reply to From a group of 5 managers (Joo, Kendra, Lee, Marnie, and in the Problem Solving forum “Our goal is to find P(M and N both selected) There are two ways to approach this. Method #1: P(M and N both selected) = P(one of them is selected 1st AND the other selected 2nd) = P(one of them is selected 1st) x P(the other selected 2nd) = (2/5)(1/4) = 1/10 = 0.1 Aside: P(one of them ...” May 28, 2019 Brent@GMATPrepNow posted a reply to Car X is 40 miles west of Car Y. Both cars are traveling in the Problem Solving forum “Let''s let Car X''s original position be the initial starting point. So, when Car X is at the initial starting point, Car Y has already traveled 40 miles. My word equation involves the conditions when Car X catches up to Car Y. At that point, we can say: Car X''s TOTAL distance traveled = ...” May 27, 2019 Brent@GMATPrepNow posted a reply to Gita is 12 years older than Harvey. In 4 years, Gita will be in the Problem Solving forum “Gita is 12 years older than Harvey. Let x = Harvey''s PRESENT age Let x + 12 = Gita''s PRESENT age In 4 years, . . . . x + 4 = Harvey''s age IN FOUR YEARS (x + 12) + 4 = Gita''s age IN FOUR YEARS . . . Gita will be twice as old as Harvey. So: (Gita''s age IN 4 YEARS) = 2(Harvey''s ...” May 26, 2019 Brent@GMATPrepNow posted a reply to Al and Ben are drivers for SD Trucking Company. One snowy da in the Problem Solving forum “Let''s start with a "word equation" (Ben''s travel distance) + (Al''s travel distance) = 240 miles Let t = Al''s travel time (in hours) So, t + 3= Ben''s travel time (since Ben spent 3 more hours driving) Distance = (rate)(time) So, our word equation becomes... (20)(t + 3) = ...” May 24, 2019 Brent@GMATPrepNow posted a reply to What is x in the diagram below? in the Problem Solving forum “The important thing to recognize here is that there are two SIMILAR TRIANGLES hiding in this diagram. http://s24.postimg.cc/50bvp89dt/sim_tri.jpg Notice that these two triangles share both a 90-degree angle AND the angle I''ve denoted with a purple dot. Since the 3 angles in each triangle must ...” May 24, 2019 Brent@GMATPrepNow posted a reply to j, k, m, x, y and z are positive integers. When j is divided in the Problem Solving forum “Useful remainder property: When positive integer N is divided by positive integer D, the remainder R is such that 0 ≤ R < D For example, if we divide some positive integer by 7, the remainder will be 6, 5, 4, 3, 2, 1, or 0 When j is divided by k, the remainder is m The above property ...” May 23, 2019 Brent@GMATPrepNow posted a reply to Challenge question: Is positive integer p even? in the Data Sufficiency forum “------ASIDE--------------------- Here''s a useful rule: If the prime factorization of N = (p^a)(q^b)(r^c) . . . (where p, q, r, etc are different prime numbers), then N has a total of (a+1)(b+1)(c+1)(etc) positive divisors. Example: 14000 = (2^4)(5^3)(7^1) So, the number of positive divisors ...” May 22, 2019 Brent@GMATPrepNow posted a new topic called j, k, m, x, y and z are positive integers. When j is divided in the Problem Solving forum “j, k, m, x, y and z are positive integers. When j is divided by k, the remainder is m. When x is divided by y, the remainder is z. If ky = 75, which of the following CANNOT be the value of mz? i) 49 ii) 50 iii) 56 A) iii only B) i and ii C) i and iii D) ii and iii E) i, ii and iii ...” May 22, 2019 Brent@GMATPrepNow posted a reply to If n is an integer greater than 6, which of the following in the Problem Solving forum “One approach is to test values If n = 7, we get: (A) 7(7 + 1)(7 – 4) = (7)(8)(3). Definitely divisible by 3. KEEP (B) 7(7 + 2)(7 – 1) = (7)(9)(6). Definitely divisible by 3. KEEP (C) 7(7 + 3)(7 – 5) = (7)(10)(4). NOT divisible by 3. ELIMINATE. (D) 7(7 + 4)(7 – 2) = (7)(11)(5). NOT ...” May 22, 2019 Brent@GMATPrepNow posted a reply to Question from mba.com mock test in the Problem Solving forum “The temperature of a certain cup of coffee 10 minutes after it was poured was 120 degrees Fahrenheit. So, 120 = 120 * 2^10)] + 60 Divide both sides by 60: 2 = 2 * 2^ f = 120 * 2^ The temperature of the coffee 30 minutes after it was poured was how many degrees Fahrenheit? f = 120 * 2^30)] + ...” May 21, 2019 Brent@GMATPrepNow posted a reply to OG #132 in the Problem Solving forum “We need to be able to create AT LEAST 12 codes (to represent the 12 countries). Let''s test the options. Can we get 12 or more color codes with 4 colors? Let''s see . . . 1-color codes = 4 (since there are 4 colors) 2-color codes = We need to choose 2 colors from 4. This can be ...” May 21, 2019 Brent@GMATPrepNow posted a reply to ps 500 test27 #16 in the Problem Solving forum “One approach: Salary Mary''s NET salary was x - y dollars (because Mary gave John y dollars) John''s NET salary was x + y dollars Hours worked Mary worked 8 hours John worked 10 hours In the end, John and Mary received the SAME hourly wage. So, John''s hourly wage = Mary''s ...” May 21, 2019 Brent@GMATPrepNow posted a reply to problem to solve in the Problem Solving forum “What we really have here is an algebra question requiring us to combine like terms. First, notice that K + K = 2K Using the same logic, 2^5 + 2^5 = 2(2^5) = (2^1)(2^5) = 2^6 Similarly, notice that M + M + M = 3M Using the same logic, 3^5 + 3^5 + 3^5 = 3(3^5) = (3^1)(3^5) = 3^6 So, 2^5 + ...” May 21, 2019 Brent@GMATPrepNow posted a reply to test 39 #13 in the Problem Solving forum “Here''s a related question to practice with: https://www.beatthegmat.com/intensity-scale-readings-t273997.html Cheers, Brent” May 21, 2019 Brent@GMATPrepNow posted a reply to test 38 #15 in the Problem Solving forum “red = 7 yellow = 5 green = 3 blue = 2 147,000 = (2)(2)(2)(3)(5)(5)(5)(7)(7) So, there are 3 blue beads, 1 green bead, 3 yellow beads and 2 red beads. Cheers, Brent” May 21, 2019 Brent@GMATPrepNow posted a reply to test35 # 15 in the Problem Solving forum “We want to determine how many integers end in 13 For example, 324713, 324813, 324913, 325013, . . . etc. Recognize that, for every 100 consecutive integers, only 1 will end in 13. There are 133,900 integers between 324,700 and 458,600 (since 458,600 - 324,700 = 133,900) Of those 133,900 ...” May 21, 2019 Brent@GMATPrepNow posted a reply to Help on PS problem- GMATprep in the Problem Solving forum “Let''s test the values using x = 0 So, we can reword the question as, For which of the following functions is f(0)=f(1-0) In other words, we''re looking for a function such that f(0) = f(1) A) f(x)=1-x f(0)=1-0 = 1 f(1)=1-1 = 0 Since f(0) doesn''t equal f(1), eliminate A B) f(x) = 1 - ...” May 21, 2019 Brent@GMATPrepNow posted a reply to Probability in the Problem Solving forum “We want: a) # of teams that include both John and Peter b) total # of 5-person teams possible a) # of teams that include both John and Peter Put John and Peter on the team (this can be accomplished in 1 way) Select the remaining 3 team-members from the remaining 7 players (this can be ...” May 21, 2019 Brent@GMATPrepNow posted a reply to Mr. Jones spends$ 25 on movie tickets for a party of adults in the Data Sufficiency forum
“ Given: Mr. Jones spends $25 on movie tickets for a party of adults and children. Target question: How many children''s tickets did he buy? Statement 1: Adult movie tickets cost$3 each and children''s tickets cost $2 each. There are several scenarios that satisfy statement 1. Here are ...” May 21, 2019 Brent@GMATPrepNow posted a reply to A collection of 16 coins, each with a face value of either in the Problem Solving forum “Let D = the NUMBER of 10-cent coins Let Q = the NUMBER of 25-cent coins Notice that the VALUE of Q 25-cent coins = ($0.25)Q For example, the VALUE of six 25-cent coins = ($0.25)6 =$1.50 And the VALUE of ten 25-cent coins = ($0.25)10 =$2.50 etc Likewise, the VALUE of D 10-cent coins = ...”
May 21, 2019
Brent@GMATPrepNow posted a new topic called Challenge question: Is positive integer p even? in the Data Sufficiency forum
“Is positive integer p even? (1) 4p has twice as many positive divisors as p has (2) 8p has 3 positive divisors more than p has Answer: A Source: www.gmatprepnow.com Difficulty level: 700+”
May 20, 2019
Brent@GMATPrepNow posted a reply to In the figure above, if A, B, and C are the areas, respectiv in the Data Sufficiency forum
“Key concept: We''re told that the area of the BLUE circle = the area of the RED circle https://i.imgur.com/AZaIFeU.png This means we can say: A + B = B + C Now onto the question..... Target question: What is the value of B + C ? Statement 1: A + 2B + C = 24 Rewrite this as: (A + B) ...”
May 17, 2019
Brent@GMATPrepNow posted a reply to Bite-sized video lessons from GMAT Prep Now in the GMAT Math forum
“Data Sufficiency lesson #7: - The Table Method Video : https://www.youtube.com/watch?v=lYfTiRIG_k4 Cheers, Brent”
May 16, 2019
Brent@GMATPrepNow posted a reply to If Mary always takes the same route to work, how long did it in the Data Sufficiency forum
“Target question: How long did it take Mary to get to work on Friday? Statement 1: It took Mary 20 minutes to get to work on Thursday. Clearly, we cannot use this information to answer the target question with certainty. Statement 1 is NOT SUFFICIENT Statement 2: Mary''s average speed ...”
May 15, 2019
Brent@GMATPrepNow posted a reply to x-4=z y-x=8 8-z=t For the system of equations given, what in the Data Sufficiency forum
“Target question: What is the value of z? Statement 1: x = 7 Scanning the three given equations, we see that equation i is all we need to determine the value of z i) x - 4 = z Replace x with 7 to get: 7 - 4 = z So, z = 3 Since we can answer the target question with certainty, statement 1 ...”
May 14, 2019
Brent@GMATPrepNow posted a reply to In triangle JKL shown above, what is the length of segment in the Data Sufficiency forum
“KEY CONCEPT: 30-60-90 triangles are known as special right triangles, and we know quite a bit about this kind of triangle Target question: What is the length of segment JL ? Statement 1: JK = 10 https://i.imgur.com/sKEFT1R.png Compare ΔJKL with the BASE 30-60-90 triangle. Their ...”
May 13, 2019
Brent@GMATPrepNow posted a reply to A line that passes through (–1, –4) and (3, k) has a slo in the Problem Solving forum
“Slope of line between the points (x1, y1) and (x2, y2) = (y2 - y1)/(x2 - x1) So, we can write: k = [k - (-4)]/[3 - (-1)] Simplify: (k + 4)/4 = k Multiply both sides by 4 to get: k + 4 = 4k Subtract k from both sides to get: 4 = 3k Divide both sides by 3 to get: 4/3 = k Answer: C Cheers, ...”
May 13, 2019
Brent@GMATPrepNow posted a reply to If the two digit integers M and N are positive and have the in the Problem Solving forum
“This question relies on our ability to determine the VALUE of any 2-digit number. For example, what is the VALUE of 83? For many of us, it has been a very long time since we examined this (we learned this when we were 5 or 6). Most of us just say that 83 has a value of 83, but 83 is really just ...”
May 13, 2019
Brent@GMATPrepNow posted a reply to If n is an integer greater than 10, then the expression (n^2 in the Problem Solving forum
“-----ASIDE--------------------- There''s a nice rule says: The product of k consecutive integers is divisible by k, k-1, k-2,...,2, and 1 So, for example, the product of any 5 consecutive integers will be divisible by 5, 4, 3, 2 and 1 Likewise, the product of any 11 consecutive integers will be ...”
May 12, 2019
Brent@GMATPrepNow posted a reply to If x and y are the lengths of the legs of a right triangle, in the Data Sufficiency forum
“ Given: x and y are the lengths of the legs of a right triangle We have something like this: https://i.imgur.com/VxCexHO.png Target question: What is the value of xy? Statement 1: The hypotenuse of the triangle is There are infinitely-many different right triangles that meet this ...”
May 11, 2019
Brent@GMATPrepNow posted a reply to In how many different ways can a soccer team finish the in the Problem Solving forum
“Question rephrased: In how many different ways can we arrange the letters WWWLLD -------------ASIDE-------------------------------------- When we want to arrange a group of items in which some of the items are identical, we can use something called the If there are n objects where A of them are ...”
May 11, 2019
Brent@GMATPrepNow posted a reply to Jones has worked at Firm X twice as many years as Green in the Data Sufficiency forum
“We can also solve the question using one variable Given: Jones has worked at Firm X twice as many years as Green, and Green has worked at Firm X four years longer than Smith. Let G = the number of years Green worked at Firm X So, G - 4 = the number of years Smith worked at Firm X (since ...”
May 10, 2019
Brent@GMATPrepNow posted a reply to In the below addition A, B, C, D, E, F, and G represent the in the Problem Solving forum
“If we add two 2-digit numbers and the sum is a 3-digit number, then the 3-digit number must start with a 1. So, E = 1 In order for the sum to be a 3-digit number, A+C must be greater than 9 So, we have two options: EITHER A and C are 5 and 6, OR A and C are 4 and 6 If A and C are 5 and 6, ...”
May 10, 2019
Brent@GMATPrepNow posted a reply to If xyz ≠ 0, what is the value of in the Data Sufficiency forum
“Target question: What is the value of (x⁴z²)/(z²y²)? This is a good candidate for rephrasing the target question. Since z ≠ 0, we know that z² ≠ 0 So, we can safely take (x⁴z²)/(z²y²) and divide top and bottom by z² to get: x⁴/y² REPHRASED target question: What is the value ...”
May 9, 2019
Brent@GMATPrepNow posted a reply to Is quadrilateral PQRS a parallelogram? in the Data Sufficiency forum
“Target question: Is quadrilateral PQRS a parallelogram? If you recognize that each statement on its own is not sufficient, we can jump straight to . . . Statements 1 and 2 combined There are infinitely-many quadrilaterals that satisfy BOTH statements. Here are two: Case a: PQRS could ...”
May 9, 2019
Brent@GMATPrepNow posted a reply to A lecture course consists of 595 students. The students are in the Problem Solving forum
“In order to have an EQUAL number of students in each section, the number of students per section MUST BE A FACTOR of 595 Let''s do some prime factorization 595 = (5)(7)(17) From the prime factorization, we can see that answer choice A, B, D and E are all factors of 595 Answer: C Cheers, ...”
May 9, 2019
Brent@GMATPrepNow posted a reply to If a and b are constants, is the expression in the Data Sufficiency forum
“Target question: Is the expression defined for x = –2? This is a great candidate for rephrasing the target question. If x = -2, then the expression becomes (-2)+b/√(-2+a) There are two ways in which the expression(-2)+b/√(-2+a) is NOT defined: case i) If a = 2, then the fraction''s ...”
May 9, 2019
Brent@GMATPrepNow posted a reply to Is x = y? in the Data Sufficiency forum
“Target question: Is x = y? Statement 1: 2x/3 - y/3 = 1/3 Multiply both sides by 3 to get: 2x - y = 1 There are several values of x and y that satisfy this equation. Here are two: Case a: x = 1 and y = 1. In this case, the answer to the target question is YES, it is the case that x = y ...”
May 9, 2019
Brent@GMATPrepNow posted a reply to The figure above represents a box that has the shape of a in the Data Sufficiency forum
“Target question: What is the volume of the box? IMPORTANT: For geometry Data Sufficiency questions, we are typically checking to see whether the statements "lock" a particular angle, length, or shape into having just one possible measurement. This concept is discussed in much greater ...”
May 9, 2019
Brent@GMATPrepNow posted a reply to In the figure above, PQRT is a rectangle. What is the length in the Data Sufficiency forum
“Let''s assign some variables to some of the lengths... https://i.imgur.com/BpaiRKm.png Target question: What is the value of x? Statement 1: The area of region PQRS is 39 and TS = 6. Region PQRS is a TRAPEZOID Area of trapezoid = (height)(base1 + base2)/2 So, we get: (x)(y + z)/2 = 39 ...”
May 9, 2019
Brent@GMATPrepNow posted a reply to Charlie takes 2.5 hours to fly from Los Angeles to Mexico Ci in the Problem Solving forum
“Here''s how I would answer this in my head Average speed = total distance/total time = 1200/2.5 = 2400/5 = 4800/10 = 480 Answer: D Cheers, Brent”
May 9, 2019
Brent@GMATPrepNow posted a reply to What amount did Jean earn from the commission on her sales in the Data Sufficiency forum
“Target question: What amount did Jean earn from the commission on her sales in the FIRST HALF of 1988 ? Statement 1: In 1988 Jean''s commission was 5 percent of the total amount of her sales. We don''t know her total sales amount in 1988, AND we don''t know what happened in the FIRST HALF of ...”
May 8, 2019
Brent@GMATPrepNow posted a reply to Six shipments of machine parts were shipped from a factory o in the Data Sufficiency forum
“We might be able to solve this one faster by first converting the fractions to decimals. S1=0.25 S2=0.2 S3=0.17 (approx) S4=0.15 S5=0.13 (approx) S6=0.1 Statement 1: S2 and S4 were shipped on the first truck. First truck has 0.2 + 0.15 = 0.35 Since the first truck holds more than 0.5, ...”
May 7, 2019
Brent@GMATPrepNow posted a reply to If a and b are integers, is a^5 < 4^b ? in the Data Sufficiency forum
“\ Target question: Is a^5 > 4^b Statement 1: a³ = -27 Solve to get: a = -3 So, a^5 = (-3)^5 = -243 Since 4^b will be POSITIVE for all values of b, the answer to the target question is NO, a^5 is definitely NOT greater than 4^b Since we can answer the target question with certainty, ...”
May 7, 2019
Brent@GMATPrepNow posted a reply to Anthony and Michael sit on the six-member board of directors in the Problem Solving forum
“Let''s assume that we''re creating subcommittees. We want to place 6 people in the following spaces: _ _ _ | _ _ _ First, we place Michael in one subcommittee; it makes no difference which one: M _ _ | _ _ _ Now place Anthony. We can see that there are 5 spaces remaining. 2 spaces ...”
May 7, 2019
Brent@GMATPrepNow posted a reply to If x is 8/3 percent of y, y is what percent of x? in the Problem Solving forum
“x percent = x/100 So, 8/3 percent = (8/3)/100 = (8/3)/(100/1) = (8/3)(1/100) = 8/300 GIVEN: x is 8/3 percent of y, We can write: x = 8/300 of y In other words: x = (8/300)(y) or......: x = 8y/300 y is what percent of x? Take: x = 8y/300 Multiply both sides by 300 to get: 300x = 8y ...”
May 7, 2019
Brent@GMATPrepNow posted a reply to Last year the range of the annual salaries of the 100 employ in the Problem Solving forum
“A quick solution is to assign some values to the highest paid and lowest paid workers Let $10,000 = the lowest salary LAST YEAR Let$40,000 = the highest salary LAST YEAR This satisfies the condition that the range LAST YEAR = $30,000 If the annual salary of each of the 100 employees this ...” May 4, 2019 Brent@GMATPrepNow posted a reply to Last year the range of the annual salaries of the 100 employ in the Problem Solving forum “Hey BTGmoderatorDC, You posted this question 2 months ago: https://www.beatthegmat.com/last-year-the-range-of-the-annual-salaries-of-the-100-t306593.html Cheers, Brent” May 4, 2019 Brent@GMATPrepNow posted a reply to A certain rectangular window is twice as long as it is wide. in the Problem Solving forum “Approach #2: Algebra Let x = the width of the rectangle So, 2x = the length of the rectangle If the perimeter is 10, we can write: x + x + 2x + 2x = 10 Simplify: 6x = 10 Solve: x = 10/6 = 5/3 So, the width (x) is 5/3 And the length (2x) is 10/3 Answer: B Cheers, Brent” May 4, 2019 Brent@GMATPrepNow posted a reply to A certain rectangular window is twice as long as it is wide. in the Problem Solving forum “We COULD use algebra to solve this question. However, it''s probably faster to just test the answer choices The answer choices give us the length and width of the rectangle. So, the sum of two values will equal HALF the perimeter of the rectangle. Since we want a perimeter of 10, the ...” May 4, 2019 Brent@GMATPrepNow posted a reply to Three-fourths of the area of a rectangular lawn 30 feet wide in the Problem Solving forum “Here''s a diagram of the 30 x 40 lawn https://i.imgur.com/6dQyyQ5.png If we keep the full width (of 30 feet), then the length of the enclosure = 3/4 of 40 = 30 feet https://i.imgur.com/nRkAVRU.png So, the enclosure is a 30 by 30 square. The PERIMETER = 30 + 30 + 30 + 30 = 120 feet If ...” May 4, 2019 Brent@GMATPrepNow posted a reply to If rectangle ABCD is inscribed in the circle above, what is in the Problem Solving forum “Draw a line connecting points A and C. https://i.imgur.com/fQaxM5q.png An important circle property (see video below for more info) tells us that, if we have a 90-degree inscribed angle, then that angle must be containing ("holding") the DIAMETER of the circle. So, we know that AC = ...” May 4, 2019 Brent@GMATPrepNow posted a reply to In quadrilateral ABCD above, what is the length of AB ? in the Problem Solving forum “https://i.imgur.com/srEvM6A.png If we focus on the blue right triangle, we can EITHER recognize that legs of length 3 and 4 are part of the 3-4-5 Pythagorean triplet, OR we can apply the Pythagorean Theorem. https://i.imgur.com/L50lEKr.png Either way, we''ll see that the triangle''s ...” May 4, 2019 Brent@GMATPrepNow posted a reply to A paint mixture was formed by mixing exactly 3 colors of in the Data Sufficiency forum “Target question: How many gallons of green paint were used? Given: A paint mixture was formed by mixing exactly 3 colors of paint. By volume, the mixture was x% blue paint, y% green paint, and z% red paint. 1 gallon of blue paint and 3 gallons of red paint were used. In other words, we ...” May 2, 2019 Brent@GMATPrepNow posted a reply to If 2.00X and 3.00Y are 2 numbers in decimal form with thousa in the Data Sufficiency forum “ Given: 2.00X and 3.00Y are 2 numbers in decimal form with thousandths digits X and Y Target question: Is 3(2.00X) > 2(3.00Y)? This is a good candidate for rephrasing the target question. Since X is the thousandths digit, we can write: 2.00X = 2 + X/1000 Since Y is the thousandths ...” May 2, 2019 Brent@GMATPrepNow posted a reply to If n^m leaves a remainder of 1 after division by 7 for all in the Problem Solving forum “The most important piece of information is here: "for all positive integers n that are not multiples of 7" Since 2 is not a multiple of 7, then it must be the case that, for a particular value of m, 2^m leaves a remainder of 1 after division by 7 Let''s check the answer choices.... ...” May 1, 2019 Brent@GMATPrepNow posted a reply to If x is an integer greater than 0, what is the remainder in the Data Sufficiency forum “Target question: What is the remainder when x is divided by 4 ? Statement 1: The remainder is 3 when x + 1 is divided by 4. ------ASIDE---------------------- There''s a nice rule that says, "If N divided by D equals Q with remainder R, then N = DQ + R" For example, since 17 ...” May 1, 2019 Brent@GMATPrepNow posted a reply to What number is 6 more than x + y ? in the Data Sufficiency forum “Target question: What is the value of x + y + 6? Statement 1: y is 3 less than x. We can write: y = x - 3 There are several values of x and y that satisfy this equation. Here are two: Case a: x = 3 and y = 0. In this case, the answer to the target question is x + y + 6 = 3 + 0 + 6 = 9 ...” May 1, 2019 Brent@GMATPrepNow posted a reply to Is the average (arithmetic mean) of the numbers x, y, and z in the Data Sufficiency forum “Target question: Is the average (arithmetic mean) of the numbers x, y, and z greater than z? This is a good candidate for rephrasing the target question. Rewrite the question as "Is (x + y + z)/3 > z?" Multiply both sides by 3 to get: "Is x + y + z > 3z?" Subtract z ...” May 1, 2019 Brent@GMATPrepNow posted a reply to Every object in a box is either a sphere or a cube, and ever in the Data Sufficiency forum “Target question: How many objects are in the box? Given: Every object in a box is either a sphere or a cube, and every object in the box is either red or green. We can solve this using the Double Matrix Method. This technique can be used for most questions featuring a population in which ...” May 1, 2019 Brent@GMATPrepNow posted a reply to What is the remainder when the positive integer n is divided in the Data Sufficiency forum “Target question: What is the remainder when the positive integer n is divided by 5 ? Statement 1: When n is divided by 3, the quotient is 4 and the remainder is 1. There''s a nice rule that says, "If N divided by D equals Q with remainder R, then N = DQ + R" For example, since 17 ...” April 30, 2019 Brent@GMATPrepNow posted a reply to Is n equal to zero? in the Data Sufficiency forum “Target question: Is n equal to zero? Statement 1: The product of n and some nonzero number is 0 (n)(non-zero number) = 0 This means n must be 0 Since we can answer the target question with certainty, statement 1 is SUFFICIENT Statement 2: The sum of n and 0 is 0 If n + 0 = 0, we can ...” April 30, 2019 Brent@GMATPrepNow posted a reply to If r and s are positive numbers and θ is one in the Data Sufficiency forum “ Given: r and s are positive numbers and θ is one of the operations, +, −, ×, or ÷ Target question: Which operation is θ ? Statement 1: If r = s, then r θ s = 0 Keep in mind that r and s are POSITIVE So, we have POSITIVE θ POSITIVE = 0 POSITIVE + POSITIVE ≠ 0 So, θ cannot ...” April 30, 2019 Brent@GMATPrepNow posted a reply to How many hours does it take Jennifer to run y miles if she r in the Problem Solving forum “time = distance/rate So, time = y/x Answer: B Cheers, Brent” April 30, 2019 Brent@GMATPrepNow posted a reply to If x = 5 – 4k and y = 5k – 3, then for what value of k d in the Problem Solving forum “We want: x = y Replace values with their equivalents: 5 - 4k = 5k - 3 Add 4k to both sides: 5 = 9k - 3 Add 3 to both sides: 8 = 9k Divide both sides by 9 to get: 8/9 = k Answer: B Cheers, Brent” April 30, 2019 Brent@GMATPrepNow posted a reply to If a school district paid a total of$35 per desk for x desk in the Data Sufficiency forum
“ Given: School district paid a total of $35 per desk for x desks and a total of$30 per table for y tables So, the TOTAL amount paid = 35x + 30y. Target question: What was the total amount that the district paid for these desks and tables?? Statement 1: The total amount the district ...”
April 29, 2019
Brent@GMATPrepNow posted a reply to In a sequence of numbers in which each term is 2 more than in the Data Sufficiency forum
“ Given: Sequence of numbers is such that each term is 2 more than the preceding term Target question: What is the value of term_4? Statement 1: The last term is 90. We have no idea how many terms there are in the sequence. So, the last term could be term_5 or term_9 or term_12 or . . . ...”
April 29, 2019
Brent@GMATPrepNow posted a reply to Is the integer p divisible by 5 ? in the Data Sufficiency forum
“Target question: Is the integer p divisible by 5? Statement 1: p is divisible by 10. If p is divisible by 10, we can write: p = 10k, for some integer k. Rewrite this as: p = (5)(2)(k) This tells us that p is a multiple of 5, which means p must be divisible by 5 Since we can answer the ...”
April 29, 2019
Brent@GMATPrepNow posted a reply to If R, S, and T are points on a line in the Data Sufficiency forum
“ Given: R, S, and T are points on a line, and if R is 5 meters from T and 2 meters from S There are 4 possible scenarios that meet the above conditions: https://i.imgur.com/kOeqUfZ.png Target question: How far is S from T? Statement 1: R is between S and T. When we check the 4 ...”
April 29, 2019
Brent@GMATPrepNow posted a reply to If m and n are integers, what is the value of m + n ? in the Data Sufficiency forum
“ Given: m and n are integers Target question: What is the value of m + n ? Statement 1: (x + m)(x + n) = x² + 5x + mn and x ≠ 0. Use FOIL to expand the left side: x² + nx + mx + mn = x² + 5x + mn Factor the two middle terms: x² + x(n + m) + mn = x² + 5x + mn At this point, we ...”
April 29, 2019
Brent@GMATPrepNow posted a reply to If a and b are integers, and b > 0, does (a−1)/(b+1) = in the Data Sufficiency forum
“ Given: a and b are integers, and b > 0 Target question: Does (a - 1)/(b + 1) = a/b? This is a good candidate for rephrasing the target question. Take the equation: (a - 1)/(b + 1) = a/b Cross multiply to get: (b)(a - 1) = (a)(b + 1) Expand both sides to get: ab - b = ab + a ...”
April 29, 2019
Brent@GMATPrepNow posted a reply to Is the sum of two integers divisible by 10 ? in the Data Sufficiency forum
“Target question: Is the sum of two integers divisible by 10 ? Statement 1: One of the integers is even. We only have information about ONE number. Statement 1 is NOT SUFFICIENT Statement 2: One of the integers is a multiple of 5. We only have information about ONE number. Statement 2 ...”
April 29, 2019
Brent@GMATPrepNow posted a reply to If p, r, and s are consecutive integers in ascending in the Data Sufficiency forum
“ Given: p, r, and s are consecutive integers in ascending order and x is the average (arithmetic mean) of the three integers Since p, r and s are EQUALLY spaced, the mean of the 3 numbers = the median of the 3 numbers. Since p < r < s, we know that r = the mean = the median. In other ...”
April 29, 2019
Brent@GMATPrepNow posted a reply to Three children inherited a total of X dollars. If the oldest in the Data Sufficiency forum
“ Given: Three children inherited a total of X dollars. The oldest child inherited $7,000 more than the youngest child, and the youngest child inherited$9,000 less than the middle child Let y = the amount the YOUNGEST child received So, y + 7000 = the amount the OLDEST child received And y + ...”
April 29, 2019
Brent@GMATPrepNow posted a reply to Is x<y? in the Data Sufficiency forum
“Target question: Is x < y? Statement 1: z< y No information about x Statement 1 is NOT SUFFICIENT Statement 2: z < x No information about y Statement 2 is NOT SUFFICIENT Statements 1 and 2 combined The combined statements tell us that x and y are both greater than z ...”
April 28, 2019
Brent@GMATPrepNow posted a reply to What is the value of a^4 - b^4? in the Data Sufficiency forum
“Target question: What is the value of a⁴ - b⁴? NOTE: a⁴ - b⁴ is a difference of square, which we can factor. a⁴ - b⁴ = (a² - b²)(a² + b²) So, we can REPHRASE the target question as... REPHRASED target question: What is the value of (a² - b²)(a² + b²)? Statement 1: ...”
April 28, 2019
Brent@GMATPrepNow posted a reply to Which of the following could be the equation of line m? in the Problem Solving forum
“First off, we can eliminate answer choice D, since y = 2 is the equation of a HORIZONTAL line, and the given line is NOT horizontal. Next, we can eliminate answer choice E, since x = -2 is the equation of a VERTICAL line, and the given line is NOT vertical. Now notice that line m has a ...”
April 28, 2019
Brent@GMATPrepNow posted a reply to If S is a set of odd integers and 3 and -1... in the Data Sufficiency forum
“ Given: S is a set of odd integers and 3 and –1 are in S Target question: Is –15 in S ? Statement 1: 5 is in S So far, set S looks like this: {-1, 3, 5, . . . .} So, -15 may or may not be in set S Since we cannot answer the target question with certainty, statement 1 is NOT ...”
April 28, 2019
Brent@GMATPrepNow posted a reply to If r and s are positive integers... in the Data Sufficiency forum
“ Given: r and s are positive integers Target question: Is r + s even? Statement 1: r is even. Since we have no information about s, we cannot determine whether r + s is even Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT Statement 2: s is ...”
April 28, 2019
Brent@GMATPrepNow posted a reply to When positive integer k is divided by 5, the remainder is 2. in the Problem Solving forum
“When it comes to remainders, we have a nice rule that says: If N divided by D leaves remainder R, then the possible values of N are R, R+D, R+2D, R+3D,. . . etc. For example, if k divided by 5 leaves a remainder of 1, then the possible values of k are: 1, 1+5, 1+(2)(5), 1+(3)(5), ...”
April 28, 2019
Brent@GMATPrepNow posted a reply to Is the integer x a 3-digit integer? in the Data Sufficiency forum
“Target question: Is the integer x a 3-digit integer? Statement 1: x is the square of an integer. Let''s TEST some values. There are several values of x that satisfy statement 1. Here are two: Case a: x = 10² = 100. In this case, the answer to the target question is YES, x IS a 3-digit ...”
April 28, 2019
Brent@GMATPrepNow posted a reply to If the 1st term of a sequence is 0 and the 2nd term is 1... in the Data Sufficiency forum
“ Given: term1 = 0 and term2 = 1 Target question: Does term5 equal 2? Once we scan the two statements, we can probably jump straight to . . . Statements 1 and 2 combined There are several possible sequences that satisfy BOTH statements. Here are two: Case a: {0, 1, 2, 0, 2,...}. In ...”
April 28, 2019
Brent@GMATPrepNow posted a reply to Is the sum of four particular integers even? in the Data Sufficiency forum
“Some important rules: #1. ODD +/- ODD = EVEN #2. ODD +/- EVEN = ODD #3. EVEN +/- EVEN = EVEN #4. (ODD)(ODD) = ODD #5. (ODD)(EVEN) = EVEN #6. (EVEN)(EVEN) = EVEN Target question: Is the sum of four particular integers even? Statement 1: Two of the integers are odd and two are even. ...”
April 28, 2019
Brent@GMATPrepNow posted a reply to If 90/k is an integer, is k an integer? in the Data Sufficiency forum
“ Given: 90/k is an integer Target question: Is k an integer? Statement 1: k > 1 Let''s TEST some values. There are several values of k that satisfy statement 1. Here are two: Case a: k = 10. Notice that 90/k = 90/10 = 9, which is an integer. In this case, the answer to the target ...”
April 27, 2019
Brent@GMATPrepNow posted a reply to For a recent play performance, the ticket prices were $25 in the Data Sufficiency forum “Target question: How many of the tickets sold were for adults? Given: A total of 500 tickets were sold for the performance Let C = # of child tickets sold Let A = # of adult tickets sold So, C + A = 500 Statement 1: Revenue from ticket sales for this performance totaled$10,500 In other ...”
April 27, 2019
Brent@GMATPrepNow posted a reply to The arithmetic mean of a data set is 46 and the standard in the Problem Solving forum
“-----------ASIDE----------------- A little extra background on standard deviations above and below the mean If, for example, a set has a standard deviation of 4, then: 1 standard deviation = 4 2 standard deviations = 8 3 standard deviations = 12 1.5 standard deviations = 6 0.25 ...”
April 27, 2019
Brent@GMATPrepNow posted a reply to In the town of Z, the town lion roars on some days and not in the Data Sufficiency forum
“Target question: What is the probability that on that day, either the town lion roared or it rained? This is a good candidate for rephrasing the target question. This is an OR probability. The OR probability rule says, P(A or B) = P(A) + P(B) - P(A and B) So, P(rained or roared) = P(rained) + ...”
April 27, 2019
Brent@GMATPrepNow posted a reply to If 20 percent of x is 5y, and y = 7, what is 60 percent in the Problem Solving forum
“GIVEN: 20 percent of x = 5y This means: 40 percent of x = 10y And: 60 percent of x = 15y Since y = 7, we can write: 60 percent of x = 15(7) = 105 Answer: A”
April 27, 2019
Brent@GMATPrepNow posted a reply to Is x^2 > 15? in the Data Sufficiency forum
“Target question: Is x² > 15? Statement 1: x > -4 Let''s TEST some values. There are several values of x that satisfy statement 1. Here are two: Case a: x = -1. In this case, x² = (-1)² = 1. So, the answer to the target question is NO, x² is NOT greater than 15 Case b: x = ...”
April 27, 2019
Brent@GMATPrepNow posted a reply to If digit $$h$$ is the hudredths' digit in the decimal in the Data Sufficiency forum
“ Given: Digit h is the hundredths digit in the decimal d=0.2h6 Target question: What is the value of d, rounded to the nearest TENTH? Statement 1: d < 1/4 In other words, 0.2h6 < 0.25 This means h = 0, 1, 2, 3 or 4 If h = 0, 1, 2, 3 or 4, then 0.2h6 (aka d) rounded to the nearest ...”
April 26, 2019
Brent@GMATPrepNow posted a reply to In the rectangular coordinate system, line $$k$$ is defined in the Data Sufficiency forum
“KEY CONCEPT: If a point lies ON a line, then the coordinates (x and y) of that point must SATISFY the equation of the line. Given: Line k is defined by the equation x - 2y + n = 0 Target question: What is the value of n? Statement 1: The x-intercept of line k is 8 In other words, ...”
April 26, 2019
Brent@GMATPrepNow posted a reply to If z is a three-digit positive integer, what is the value in the Data Sufficiency forum
“ Given: z is a three-digit positive integer Target question: What is the value of the tens digit of z ? Statement 1: The tens digit of z - 91 is 3 Let''s examine two EXTREME cases z - 91 = 30 z - 91 = 39 NOTE: These are extreme cases, because 30 is the smallest 2-digit number ...”
April 25, 2019
Brent@GMATPrepNow posted a reply to Of the 60 animals on a certain farm, 2/3 are either pigs or in the Data Sufficiency forum
“Target question: How many of the animals are cows? Given: Of the 60 animals in a certain farm, 2/3 are either pigs or cows Let P = # of pigs Let C = # of cows 2/3 of 60 = 40, so we can say that P + C = 40 Statement 1: The farm has MORE THAN twice as many cows as it has pigs. In other ...”
April 25, 2019
Brent@GMATPrepNow posted a reply to Bill rides his bike to work in the morning on a route that in the Data Sufficiency forum
“Here''s a similar question to practice with: https://www.beatthegmat.com/distance-t273181.html Cheers, Brent”
April 24, 2019
Brent@GMATPrepNow posted a reply to What is the value of x? in the Data Sufficiency forum
“Target question: What is the value of x? Statement 1: 4x = 2y − 6 Divide both sides by 2 to get: 2x = y - 3 Divide both sides by 2 (again) to get: x = (y - 3)/2 As you might guess, there are infinitely many solutions to the equation x = (y - 3)/2. Here are two: Case a: y = 3, and x = 0. ...”
April 24, 2019
Brent@GMATPrepNow posted a reply to Phone plan A charges $1.25 for the first minute and$0.15 in the Problem Solving forum
“Phone plan A charges $1.25 for the first minute and$0.15 for every minute thereafter. Let x = total duration of phone call (in minutes) So, the cost of an x-minute call = $1.25 + ($0.15)(x - 1) ASIDE: I created the expression ($0.15)(x - 1) because we pay$1.25 for the FIRST minute. So, if x = ...”
April 24, 2019
Brent@GMATPrepNow posted a reply to A piece of twine of length t is cut into two pieces. in the Problem Solving forum
“A piece of twine of length t is cut into two pieces. Let x = the length of the LONGER piece in yards So, t - x = the length of the SHORTER piece in yards The length of the longer piece is 2 yards greater than 3 times the length of the shorter piece. In other words: (longer piece) = ...”
April 22, 2019
Brent@GMATPrepNow posted a reply to √(16∗20+8∗32)= in the Problem Solving forum
“One option here is to evaluate (16)(20)+(8)(32), and then find the square root of the result. That''s a bit of work. We can also apply a technique called "Multiplying by Doubling and Halving" (here''s the video: I factored out the 16 = √sqrt(xy) = (√x)(√y)] √[(16)(36)] = ...”
April 22, 2019
Brent@GMATPrepNow posted a reply to Sequence $$X$$ consists of $$825$$ terms, and each term in the Data Sufficiency forum
“Target question: What is the value of term 500? Given: Each term after the first term is 5 more than the preceding term. Statement 1: Term 515 of sequence X is -98. Since each term is 5 more than the preceding term, we know that term 514 = -103 term 513 = -108 term 512 = -113 term ...”
April 21, 2019
Brent@GMATPrepNow posted a reply to From a group of 5 managers (Joon, Kendra, Lee, Marnie and in the Problem Solving forum
“Our goal is to find P(M and N both selected) Method #1: P(M and N both selected) = P(one of them is selected 1st AND the other selected 2nd) = P(one of them is selected 1st) x P(the other selected 2nd) = (2/5)(1/4) = 1/10 = 0.1 Aside: P(one of them is selected 1st) = 2/5 because I''m ...”
April 21, 2019
Brent@GMATPrepNow posted a reply to What is the perimeter of quadrilateral Q? in the Data Sufficiency forum
“Target question: What is the perimeter of quadrilateral Q? If we recognize that each statement alone is not sufficient, we can jump straight to...... Statements 1 and 2 combined There are several quadrilaterals satisfy BOTH statements. Here are two: Case a: Q is a rectangle with width 1 ...”
April 20, 2019
Brent@GMATPrepNow posted a reply to Mary's income is 60 percent more than Tim's income, and in the Problem Solving forum
“I suggest that we choose some nice values that meet the given conditions. Tim''s income is 40 percent less than Juan''s income. Let Juan''s income = $100 40% of$100 = $40 This means Tim''s income =$100 - $40 =$60 Mary''s income is 60 percent more than Tim''s income 60% of $60 =$36 So ...”
April 20, 2019
Brent@GMATPrepNow posted a reply to For integers x and y, when x is divided by y, the remainder in the Problem Solving forum
“Since, the question asks "Which of the following must be true?", we can eliminate any answer choice that is not necessarily true. So let''s test some values that satisfy the given conditions For integers x and y, when x is divided by y, the remainder is odd. One possible case is that ...”
April 20, 2019
Brent@GMATPrepNow posted a reply to A certain library assesses fines for overdue books as follow in the Problem Solving forum
“1st day - $0.10 2nd day -$0.20 or $0.40 (double or add$0.30) $0.20 is the lesser amount 3rd day -$0.40 or $0.50 (double or add$0.30) $0.40 is the lesser amount 4th day -$0.80 or $0.70 (double or add$0.30) $0.70 is the lesser amount The correct answer is B Cheers, Brent” April 20, 2019 Brent@GMATPrepNow posted a reply to For the 5 days shown in the graph, how many kilowatt-hours in the Problem Solving forum “List the numbers in ASCENDING ORDER to get: 19, 24, 27, 29, 31. So 27 is the median. Average = (19 + 24 + 27 + 29 + 31)/5 = 130/5 = 26. The median (27) is 1 greater than the average (26). Answer: A Cheers, Brent” April 20, 2019 Brent@GMATPrepNow posted a reply to What are the coordinates of point B in the figure above? in the Data Sufficiency forum “IMPORTANT: For geometry Data Sufficiency questions, we are typically checking to see whether the statements "lock" a particular angle, length, or shape into having just one possible measurement. This concept is discussed in much greater detail in the video below. Target question: What ...” April 19, 2019 Brent@GMATPrepNow posted a reply to If (x # y) represents the remainder that results when the in the Problem Solving forum “If y > 16, (16 # y) = 16, so we need only check the values from 1 to 15 Also, we need not check the FACTORS of 16, since they will all yield a remainder of 0 We''re left with: (16 # 3) = 1 KEEP! (16 # 5) = 1 KEEP (16 # 7) = 2 (16 # 9) = 7 (16 # 10) = 6 (16 # 11) = 5 (16 # 12) = 4 (16 # ...” April 19, 2019 Brent@GMATPrepNow posted a reply to If x and y are positive integers, is x^2*y^2 even ? in the Data Sufficiency forum “Target question: Is x²y² even ? Statement 1: x + 5 is a prime number So, x+5 is a prime number greater than 5, which means x+5 must be ODD (since 2 is only even prime) If x+5 is ODD, then x must be EVEN If x is EVEN, then x²y² must be even The answer to the target question is YES, ...” April 19, 2019 Brent@GMATPrepNow posted a reply to The areas of three faces of a rectangular solid are 12, 15 a in the Problem Solving forum “Let x = the width Let y = the length Let z = the height So, the volume = xyz Area of one face = 12 We can write: xy = 12 Area of one face = 15 We can write: xz = 15 Area of one face = 20 We can write: yz = 20 Combine to get: (xy)(xz)(yz) = (12)(15)(20) Simplify: x²y²z² = 3600 ...” April 19, 2019 Brent@GMATPrepNow posted a reply to OG 2019 related questions for daily emails in the The 60-Day GMAT Study Guide forum “The OGs vary by very little with each edition. So, you can just use an earlier edition (see https://www.beatthegmat.com/official-guide-question-library-t296759.html) Cheers, Brent” April 18, 2019 Brent@GMATPrepNow posted a reply to OG 2019 related questions for daily emails in the The 60-Day GMAT Study Guide forum “Sorry, but there are no plans to update BTG''s 60-Day Study Guide to include OG2019 questions.” April 18, 2019 Brent@GMATPrepNow posted a reply to If f(2x - 1) = 4x² - 4x - 8, then f(5) = in the Problem Solving forum “Here''s one more approach: First notice that 4x² - 4x - 8 looks a lot like (2x - 1)² (2x - 1)² = (2x - 1)(2x - 1) = 4x² - 4x + 1 Now take: f(2x - 1) = 4x² - 4x - 8 Rewrite as: f(2x - 1) = 4x² - 4x + 1 - 9 = (2x - 1)² - 9 In other words, f(something) =something² - 9 In general, ...” April 18, 2019 Brent@GMATPrepNow posted a reply to y = 248 - 398x. Which of the following values of x gives in the Problem Solving forum “We can also test the answer choices.... (A) x = 200 means y = 248 - 398(200) = some number LESS THAN 248 (B) x = 100 means y = 248 - 398(100) = some number LESS THAN 248 (C) x = 0.5 means y = 248 - 398(0.5) = some number LESS THAN 248 (D) x = 0 means y = 248 - 398(0) = some number EQUAL TO ...” April 18, 2019 Brent@GMATPrepNow posted a reply to If sequence S has 120 terms, what is the 105th term of S? in the Data Sufficiency forum “Target question: What is the 105th term of S? Given: Sequence S has 120 terms Statement 1: The first term of S is −8. We have no information about the nature of the sequence. So, knowing the value of term 1 won''t help is determine the value of term 105 Since we cannot answer the ...” April 18, 2019 Brent@GMATPrepNow posted a reply to Does x + c = y + c ? in the Data Sufficiency forum “Target question: Does x + c = y + c ? This is a good candidate for rephrasing the target question. Take the equation x + c = y + c, and subtract c from both sides to get: x = y REPHRASED target question: Does x = y ? Aside: Here’s a video with tips on rephrasing the target question: ...” April 17, 2019 Brent@GMATPrepNow posted a reply to If n is a prime number greater than 3, what is the remainder in the Problem Solving forum “Choose ANY prime number greater than 3, and test it. If n = 5, then n² = 5² = 25 When 25 is divided by 12, the quotient is 2 and the remainder is 1 Answer: B Cheers, Brent” April 17, 2019 Brent@GMATPrepNow posted a reply to Is integer x odd? in the Data Sufficiency forum “Target question: Is integer x odd? Statement 1: 2x + 1 is odd There are several values of x that satisfy statement 1. Here are two: Case a: x = 1. Notice that 2x + 1 = 2(1) + 1 = 3, which is odd. In this case, the answer to the target question is YES, x IS odd Case b: x = 2. Notice that 2x ...” April 17, 2019 Brent@GMATPrepNow posted a reply to When 1,000 children were inoculated with a certain vaccine, in the Data Sufficiency forum “Target question: How many of the children developed inflammation but not fever? One approach is to use the Double Matrix Method. This technique can be used for most questions featuring a population in which each member has two characteristics associated with it (aka overlapping sets questions). ...” April 16, 2019 Brent@GMATPrepNow posted a reply to Is xy > 0? in the Data Sufficiency forum “Target question: Is xy > 0? Statement 1: x - y > -2 Let''s TEST some values. There are several values of x and y that satisfy statement 1. Here are two: Case a: x = 5 and y = 1. In this case, xy = (5)(1) = 5. So, the answer to the target question is YES, xy IS greater than 0 Case b: ...” April 16, 2019 Brent@GMATPrepNow posted a reply to If x and y are positive integers and x = 10y + 5, what is in the Problem Solving forum “GIVEN: x = 10y + 5 Factor out 5 to get: x = 5(2y + 1) We can see that x is a multiple of 5, which also means x is divisible by 5, which means the remainder will by ZERO when x is divided by 5 Answer: A Cheers, Brent” April 16, 2019 Brent@GMATPrepNow posted a reply to Last Problem in OG12 Diagnostic in the Problem Solving forum “As with all VIACs (Variables In the Answer Choices questions), we can solve this via the INPUT-OUTPUT approach (as Mitch has done) or via an ALGEBRAIC approach. Typically, when the answer choices look complex (as they do here), I find the INPUT-OUTPUT approach easier. However, the algebraic ...” April 16, 2019 Brent@GMATPrepNow posted a reply to Which of the following is equivalent to in the Problem Solving forum “Here''s another approach.... Take: $$\frac{x+y}{3}-\frac{x-y}{4}$$ Find common denominator: $$\frac{4(x+y)}{12}-\frac{3(x-y)}{12}$$ Expand numerators: $$\frac{4x+4y}{12}-\frac{3x-3y)}{12}$$ Combine fractions: $$\frac{(4x+4y)-(3x-3y)}{12}$$ Simplify numerator: $$\frac{x+7y}{12}$$ ...” April 15, 2019 Brent@GMATPrepNow posted a reply to A man spends$48 to buy 6 hamburgers and 8 colas for his in the Problem Solving forum
“Let H = price of one hamburger Let C = price of one cola A man spends $48 to buy 6 hamburgers and 8 colas for his office workers. 6H + 8C = 48 The next day, he buys 5 hamburgers and 4 colas and spends$32. 5H + 4C = 32 Assuming the prices of hamburgers and colas remain constant, what ...”
April 15, 2019
Brent@GMATPrepNow posted a reply to Alice, Benjamin, and Carol each try independently to win a in the Problem Solving forum
“P(exactly 2 win) = P(A wins and B wins and C loses OR B wins and C wins and A loses OR A wins and C wins and B loses) = P(A wins and B wins and C loses) + P(B wins and C wins and A loses) + P(A wins and C wins and B loses) Let''s calculate each probability P(A wins and B wins and C loses) = ...”
April 15, 2019
Brent@GMATPrepNow posted a reply to If n is an integer, is (100−n)n an integer? in the Data Sufficiency forum
“Target question: Is (100 - n)/n an integer? Statement 1: n > 4 Let''s TEST some values There are infinitely many values of n that satisfy statement 1. Here are two: Case a: n = 5. In this case, (100 - n)/n = (100 - 5)/5 = 95/5 = 19. So, the answer to the target question is YES, (100 - ...”
April 14, 2019
Brent@GMATPrepNow posted a reply to f(x) = x^2 - x. For which of the following values of a is in the Problem Solving forum
“GIVEN: f(x) = x² - x So, f(8) = 8² - 8 = 56 I. a = -7 So, f(-7) = (-7)² - (-7) = 56 This means f(a) ≥ f(8) Check the answer choices. . . ELIMINATE B and C II. a = -8 So, f(-8) = (-8)² - (-8) = 72 This means f(a) ≥ f(8) Check the answer choices. . . ELIMINATE A II. a = -9 ...”
April 14, 2019
Brent@GMATPrepNow posted a reply to What is the largest value of integer n such that in the Problem Solving forum
“98 = (2)(7)(7) = (2^1)(7^2) So, 98^98 = (2^1)(7^2)]^98 = (2^98)(7^196) What is the largest value of integer n such that 98^98 is divisible by 7^n? Since 98^98 = (2^98)(7^196), the largest value of n is 196 Answer: E Cheers, Brent”
April 14, 2019
Brent@GMATPrepNow posted a reply to A certain series is defined by the following recursive rule: in the Problem Solving forum
“I''m not crazy about this question. Typically, when we talk about series, Sn represents the SUM of the first n terms of that series. However, based on the official answer, Sn seems to represent the value of TERM n. Cheers, Brent”
April 12, 2019
Brent@GMATPrepNow posted a reply to Mary and Kate are running clockwise around a circular track in the Problem Solving forum
“To get a better idea of what''s happening, let''s sketch the set-up: https://i.imgur.com/SwHzFJD.png Mary is faster than Kate, we can say that Kate has a 250 meter head start. In other words, when Mary closes that 250-meter gap, she will pass Kate for the FIRST time. ...”
April 11, 2019
Brent@GMATPrepNow posted a reply to What is the sum of the cubes of the first ten positive? in the Problem Solving forum
“Let''s look for a pattern 1³ = 1 = 1² 1³ + 2³ = 9 = 3² 1³ + 2³ + 3³ = 36 = 6² 1³ + 2³ + 3³ + 4³ = 100 = 10² 1³ + 2³ + 3³ + 4³ + 5³ = 225 = 15² See the pattern yet? 1 + 2 = 3 3 + 3 = 6 6 + 4 = 10 10 + 5 = 15 First we add 2, then we add 3, then 4, then 5, etc ...”
April 11, 2019
Brent@GMATPrepNow posted a reply to If 0.00012345 is between 1/10^n and 1/10^{n-1}, what is the in the Problem Solving forum
“We need to examine powers of 10 that are smaller than AND greater than 0.00012345 We know that: 0.0001 < 0.00012345 < 0.001 Rewrite as FRACTIONS to get: 1/10,000 < 0.00012345 < 1/1,000 Rewrite as POWERS OF 10 to get: 1/10⁴ < 0.00012345 < 1/10³ We''re told that 0.00012345 ...”
April 10, 2019
Brent@GMATPrepNow posted a reply to GMAT Prep Practice Test Quant Questions #4 in the GMAT Math forum
“ Given: wx = y Target question: What is the value of xy ? Statement 1: wx²= 16 We can rewrite this as: (wx)(x) = 16 Since wx = y, we can replace wx with y to get: (y)(x) = 16 So, the answer to the target question is xy = 16 Since we can answer the target question with certainty, ...”
April 9, 2019
Brent@GMATPrepNow posted a reply to A camera lens filter kit containing 5 filters sells for $in the Problem Solving forum “2 of them are priced at$10.45 each, 2 at $12.05 each, 1 at$17.50 TOTAL cost when purchased individually = (2 x $10.45) + (2 x$12.05) + (1 x $17.50) =$20.90 + $24.10 +$17.50 = $62.50 The amount saved by purchasing the kit is what percent of the total price of the 5 filters purchased ...” April 9, 2019 Brent@GMATPrepNow posted a reply to Machine A produces pencils at a constant rate of 9000 in the Problem Solving forum “To MINIMIZE machine B''s operating time, we must MAXIMIZE the time machine A''s operating time. So, let machine A operate for the full 8 hours. In 8 hours, machine A produces 72,000 pencils So, the number of pencils machine B must make = 100,000 - 72,000 = 28,000 Time = output/rate So, ...” April 9, 2019 Brent@GMATPrepNow posted a reply to Any decimal that has only a finite number of nonzero digits in the Data Sufficiency forum “Target question: Is r/s a terminating decimal? Statement 1: 90 < r < 100 There are several pairs of values that meet this condition. Here are two: Case a: r = 91 and s = 2, in which case r/s = 91/2 = 45.5 = a terminating decimal Case b: r = 91 and s = 3, in which case r/s = 91/3 = ...” April 8, 2019 Brent@GMATPrepNow posted a reply to A sewing store buys fabric X by the bolt at the wholesale in the Data Sufficiency forum “Target question: What is the wholesale price of a bolt of fabric X? Given: Each bolt contains 50 meters of fabric X Statement 1: The store sells fabric X for$6.25 per meter. No information about the relationship between the WHOLESALE price and the RETAIL price Statement 1 is NOT ...”
April 8, 2019
Brent@GMATPrepNow posted a reply to There are 10 books on a shelf: 5 English books, 3 Spanish in the Problem Solving forum
“Let''s use the complement. That is, P(Event A happening) = 1 - P(Event A not happening) So, here we get: P( 2 different languages) = 1 - P(NOT 2 different languages) So, we can write: P(2 different languages) = 1 - P(the 2 languages are the SAME) P(the 2 languages are the SAME) P(the 2 ...”
April 8, 2019
Brent@GMATPrepNow posted a reply to Any feedback on the Orion GMAT prep? in the Helpful Resources forum
“Sorry - I know almost nothing about that company. Cheers, Brent”
April 7, 2019
Brent@GMATPrepNow posted a reply to Bite-sized video lessons from GMAT Prep Now in the GMAT Math forum
“Data Sufficiency lesson #6: - Rephrasing the Target Question Video : https://www.youtube.com/watch?v=MyG1K3ee69w Cheers, Brent”
April 7, 2019
Brent@GMATPrepNow posted a reply to In a certain game only one player can win and only one in the Data Sufficiency forum
“Target question: What is the probability that Katelyn wins at least one of the 3 games? This is a good candidate for rephrasing the target question. In order to determine P(Katelyn wins at least one of the 3 games), we need to know the probability that Katelyn wins if they play ONE game. We ...”
April 7, 2019
Brent@GMATPrepNow posted a reply to Question of the Week - 3 (The value of the variable E is...) in the Problem Solving forum
“A fast approach is to use some estimation. E = 1/2 + 1/4 + 1/6 + 1/8 + 1/10 + 1/12 + 1/14 + 1/16 + 1/18 + 1/20 ≈ 0.5 + 0.25 + 0.15 + 0.1 + 0.1 + 0.1 + 0.05 + 0.05 + 0.05 + 0.05 ≈1.4 Which of the following can be a possible value of the reciprocal of E? The reciprocal of E ...”
April 7, 2019
Brent@GMATPrepNow posted a reply to Is the positive integer x an even number? in the Data Sufficiency forum
“OA=E Target question: Is x an even number? Jump straight to..... Statements 1 and 2 combined There are infinitely many values of x that satisfy BOTH statements. Here are two: Case a: x = 32. In this case, the answer to the target question is YES, x IS an even number Case b: x = 17. ...”
April 6, 2019
Brent@GMATPrepNow posted a reply to During a trip that they took together, Carmen, Juan, Maria, in the Problem Solving forum
“Let x = the number of miles Rafael drove Average = 80 So, (72 + 78 + 83 + x)/4 = 80 Multiply both sides by 4 to get: 72 + 78 + 83 + x = 320 Simplify: 233 + x = 320 Solve: x = 87 Answer: D”
April 6, 2019
Brent@GMATPrepNow posted a reply to If a certain animated cartoon consists of a total of 17,280 in the Data Sufficiency forum
“Target question: How many minutes will it take to run the cartoon? Given: cartoon consists of a total of 17,280 frames Statement 1: The cartoon runs without interruption at the rate of 24 frames per second. Time = (output)/(rate) So, time = (17,280 frames)/(24 frames per second) NOTE: ...”
April 6, 2019
Brent@GMATPrepNow posted a reply to While a family was away on vacation, they paid in the Problem Solving forum
“..... paid a neighborhood boy $11 per week to mow their lawn... So, in 3 weeks, the amount the family paid for lawn-moving = (3 weeks)($11/week) = $33 ...the family paid$4 per DAY to feed and walk their dog... 3 weeks = 21 DAYS So, the amount the family paid for dog care = (21 days)($4/day) = ...” April 6, 2019 Brent@GMATPrepNow posted a reply to Last year$48,000 of a certain store's profit was shared in the Problem Solving forum
“Each owner received 3 times as much as each employee Let E = the amount (in dollars) that ONE employee received So, 3E = the amount (in dollars) that ONE owner received Last year $48,000 of a certain store''s profit was shared by its 2 owners and their 10 employees. In other words: 3E + 3E + ...” April 6, 2019 Brent@GMATPrepNow posted a reply to Alice is twice as old as Brian and Cathy is 6 years in the Problem Solving forum “GIVEN: Alice is a years old Alice is twice as old as Brian This also means Brian is HALF as old as Alice So, Brian''s age = a/2 Cathy is 6 years younger than Brian So, Cathy''s age = (Brian''s age) - 6 So, Cathy''s age = (a/2) - 6 How old is Cathy in terms of a ? Cathy''s age = (a/2) - ...” April 6, 2019 Brent@GMATPrepNow posted a reply to For all numbers m and n... in the Problem Solving forum “GOAL: Find the value of 4?3 GIVEN: m?n = (2m - n)(m+ n) So, 4?3 = (2(4) - 3)(4+ 3) = (5)(7) = 35 Answer: A Cheers, Brent” April 6, 2019 Brent@GMATPrepNow posted a reply to If x and y are two points on the number line what is the in the Data Sufficiency forum “Target question: What is the value of x + y? Statement 1: 6 is halfway between x and y. KEY CONCEPT: The average (arithmetic mean) of 2 numbers is HALFWAY between those 2 numbers. For example, the average of 1 and 9 is 5. Notice that 5 is HALFWAY between 1 and 9. So, statement is ...” April 6, 2019 Brent@GMATPrepNow posted a reply to The residents of Town X participated in a survey to in the Problem Solving forum “---------ASIDE-------------------- A little extra background on standard deviations above and below the mean If, for example, a set has a standard deviation of 4, then: 1 standard deviation = 4 2 standard deviations = 8 3 standard deviations = 12 1.5 standard deviations = 6 0.25 ...” April 6, 2019 Brent@GMATPrepNow posted a reply to In the xy-coordinate system, line k has slope 1/2 and passes in the Problem Solving forum “Let''s first determine the equation of line k A quick approach is the write the equation of line k in slope y-intercept form: y = mx + b, where m = slope and b = y-intercept. We''re told that the slope = 0.5 and the point (0,5) tells us that the y-intercept is 5 So, the equation of line k is: ...” April 6, 2019 Brent@GMATPrepNow posted a reply to In a certain office, the ratio of men to women is 3/4. in the Problem Solving forum “Another approach: Let M = number of men CURRENTLY in the office Let W = number of women CURRENTLY in the office In a certain office, the ratio of men to women is CURRENTLY 3/4. We can write: M/W = 3/4 Cross multiply to get: 4M = 3W Rewrite as: 4M - 3W = 0 If 10 men were added to the ...” April 6, 2019 Brent@GMATPrepNow posted a reply to In a certain office, the ratio of men to women is 3/4. in the Problem Solving forum “In a certain office, the ratio of men to women is 3/4. This tells us that, out of EVERY 7 people in the office, 3 are men and 4 are women. It also tells us that the TOTAL number of men and women currently in the office is divisible by 7 When we check the answer choices, we see that A, B and E ...” April 6, 2019 Brent@GMATPrepNow posted a reply to In the diagram above, points A, B, C, D, and E represent the in the Problem Solving forum “points A, B, C, D, and E represent the five teams in a certain league in which each team must play each of the other teams exactly once. Let''s first determine the total number of games that will be played. There are 5 teams, so each team will play 4 games (since a team can''t play itself) So, ...” April 6, 2019 Brent@GMATPrepNow posted a reply to John and Mary were each paid x dollars in advance to do a in the Problem Solving forum “One approach: Salary Mary''s NET salary was x - y dollars (because Mary gave John y dollars) John''s NET salary was x + y dollars Hours worked Mary worked 8 hours John worked 10 hours In the end, John and Mary received the SAME hourly wage. So, John''s hourly wage = Mary''s ...” April 5, 2019 Brent@GMATPrepNow posted a reply to On a certain sightseeing tour, the ratio of the number in the Data Sufficiency forum “Let W = # of women Let M = # of men Let C = # of children Target question: What is the value of M? Given: The ratio of the number of women to the number of children was 5 to 2 In other words, W : C = 5 : 2 Statement 1: On the sight-seeing tour, the ratio of the number of children to ...” April 5, 2019 Brent@GMATPrepNow posted a reply to Five friends - Ross, Phoebe, Chandler, Joey, and Monica in the Problem Solving forum “Take the task of feeding the 5 friends and break it into stages. We’ll begin with the most restrictive stage(s). Stage 1: Select a pizza for Phoebe Since Phoebe will only eat Margherita pizza, there''s only 1 pizza we can serve her. So, we can complete stage 1 in 1 way Stage 2: ...” April 5, 2019 Brent@GMATPrepNow posted a reply to The y intercept of a line L is 4. If the slope of L is in the Problem Solving forum “Let''s draw a bunch of lines with a negative slope AND have a y-intercept of 4 (ie, passes through the point (0,4)) We get: http://i1168.photobucket.com/albums/r500/GMATPrepNow/x-int_zpsswbinqns.png As we can see, the x-intercept can have ANY POSITIVE value. So, the x-intercept COULD be 6, ...” April 5, 2019 Brent@GMATPrepNow posted a reply to In the rectangular solid above, if each dimession of the in the Data Sufficiency forum “Here''s a very similar (official) practice question: https://www.beatthegmat.com/volume-of-rectangular-solid-t273956.html Cheers, Brent” April 5, 2019 Brent@GMATPrepNow posted a reply to Is x < 0? in the Data Sufficiency forum “Target question: Is x < 0? Two important rules: ODD exponents preserve the sign of the base. So, (NEGATIVE)^(ODD integer) = NEGATIVE and (POSITIVE)^(ODD integer) = POSITIVE An EVEN exponent always yields a positive result (unless the base = 0) So, (NEGATIVE)^(EVEN integer) = ...” April 5, 2019 Brent@GMATPrepNow posted a reply to In the sequence S, each term after the first is twice the in the Problem Solving forum “term1 = 3 term2 = (3)(2) = (3)(2¹) term3 = (3)(2)(2) = (3)(2²) term4 = (3)(2)(2)(2) = (3)(2³) term5 = (3)(2)(2)(2)(2) = (3)(2⁴) . . term14 = (3)(2^13) term15 = (3)(2^14) term16 = (3)(2^15) What is the sum of the 14th, 15th, and 16th terms in sequence S? Sum = (3)(2^13) + ...” April 5, 2019 Brent@GMATPrepNow posted a reply to If x, y, and d are integers and d is odd, are both x and y in the Data Sufficiency forum “ Given: x, y, and d are integers and d is odd Target question: Are both x and y divisible by d? Statement 1: x+y is divisible by d. Let''s TEST some values. There are several values of x, y and d that satisfy statement 1. Here are two: Case a: x = 6, y = 9 and d = 3. Notice that 6+9 = ...” April 4, 2019 Brent@GMATPrepNow posted a reply to m and n are positive integers. Are m and n consecutive integ in the Data Sufficiency forum “ Given: m and n are positive integers. Target question: Are m and n consecutive integers? Statement 1: m² + n² = 5 Since m and n are positive integers, there are only two possible solutions: Solution #1: m = 1 and n = 2 Solution #2: m = 2 and n = 1 In BOTH possible cases, the ...” April 3, 2019 Brent@GMATPrepNow posted a reply to If Norbert can cut up one plastic six pack container in 30 in the Problem Solving forum “We can solve this question by applying equivalent ratios For every 30 seconds that elapse, Norbert can cut up 1 plastic six-pack container In other words, for every 0.5 MINUTES that elapse, Norbert can cut up 1 plastic six-pack container Let t = the time (in MINUTES) to cut up 512 plastic ...” April 2, 2019 Brent@GMATPrepNow posted a reply to For what percent of those tested for a certain infection was in the Data Sufficiency forum “I just want to point out that Jay has done a perfect job employing a technique known as the Double Matrix Method. This technique can be used for most questions featuring a population in which each member has two characteristics associated with it. Here, we have a population of patients, and the ...” April 2, 2019 Brent@GMATPrepNow posted a reply to What is the number of cans that can be packed in a certain in the Data Sufficiency forum “Target question: What is the number of cans that can be packed in a certain carton? Let''s head straight to..... Statements 1 and 2 combined Consider these two conflicting cases (that satisfy BOTH statements): Case a: the dimensions of the box are numbers are 1 x 1 x 2304 (inches), in ...” April 1, 2019 Brent@GMATPrepNow posted a reply to 2+2+2^2+2^3+2^4+2^5+2^6+2^7+2^8=? in the Problem Solving forum “Let''s look for a pattern... We want: 2 + 2 + 2^2 + 2^3 + 2^4 + 2^5 + 2^6 + 2^7 + 2^8 = ? 2 + 2 + 2^2 = 4 + 4 = 8 = 2^3 So, 2 + 2 + 2^2 + 2^3 + 2^4 + 2^5 + 2^6 + 2^7 + 2^8 = 2^3 + 2^3 + 2^4 + 2^5 + 2^6 + 2^7 + 2^8 2^3 + 2^3 = 2(2^3) = 2^4 So, 2^3 + 2^3 + 2^4 + 2^5 + 2^6 + 2^7 + 2^8 = 2^4 + ...” April 1, 2019 Brent@GMATPrepNow posted a reply to If n is the smallest of three consecutive positive integers in the Problem Solving forum “There''s a nice rule says: The product of k consecutive integers is divisible by k, k-1, k-2,...,2, and 1 So, for example, the product of any 5 consecutive integers will be divisible by 5, 4, 3, 2 and 1 Likewise, the product of any 11 consecutive integers will be divisible by 11, 10, 9, . . . 3, ...” April 1, 2019 Brent@GMATPrepNow posted a reply to A collection of 36 cards consists of 4 sets of 9 cards in the Data Sufficiency forum “Target question: What is the number on the card? Given: A collection of 36 cards consists of 4 sets of 9 cards in each set are numbered 1 through 9. Statement 1: The units digit of the sum of the numbers on the remaining 35 cards is 6. 1+2+3+4+5+6+7+8+9=45 Since there are 4 sets of ...” April 1, 2019 Brent@GMATPrepNow posted a reply to If x = 1 – 2y, what is z? in the Data Sufficiency forum “Target question: What is the value of z? Given: x = 1 – 2y Statement 1: 5x + 10y + z = 5 Replace x with 1 – 2y to get: 5(1 – 2y) + 10y + z = 5 Expand: 5 - 10y + 10y + z = 5 Simplify: 5 + z = 5 Solve: z = 0 Since we can answer the target question with certainty, statement 1 is ...” April 1, 2019 Brent@GMATPrepNow posted a reply to Is x > 0? in the Data Sufficiency forum “Target question: Is x > 0? Statement 1: x² > 0 This statement doesn''t feel sufficient, so I''ll TEST some values. There are several values of x that satisfy statement 1. Here are two: Case a: x = 1. In this case, the answer to the target question is YES, it is the case that x > ...” April 1, 2019 Brent@GMATPrepNow posted a reply to If y is the smallest positive integer such that 3,150 in the Problem Solving forum “Key concept: The prime factorization of a perfect square (the square of an integer) will have an EVEN number of each prime. For example, 36 = (2)(2)(3)(3) And 400 = (2)(2)(2)(2)(5)(5) Likewise, 3150y must have an EVEN number of each prime in its prime factorization. So, 3150y = ...” April 1, 2019 Brent@GMATPrepNow posted a reply to If 3 less than twice a certain number is equal to 2 more in the Problem Solving forum “Let x be the number 3 less than twice a certain number is equal to 2 more than 3 times the number We can write: 2x - 3 = 3x + 2 So: -3 = x + 2 Solve: -5 = x 5 less than 5 times the number is 5 times the number = 5(-5) = -25 So, 5 less than 5 times the number = -25 - 5 = -30 Answer: A ...” March 31, 2019 Brent@GMATPrepNow posted a reply to Which of the following inequalities is an algebraic in the Problem Solving forum “When solving inequalities involving ABSOLUTE VALUE, there are 2 things you need to know: Rule #1: If |something| < k, then –k < something < k Rule #2: If |something| > k, then EITHER something > k OR something < -k Note: these rules assume that k is positive (A) |x| ≤ 3 ...” March 31, 2019 Brent@GMATPrepNow posted a reply to In how many ways a criket team consisting of 5 batsmen, 4 in the Problem Solving forum “Take the task of creating a cricket team and break it into stages. Stage 1: Select 5 batsmen Since the order in which we select the batsmen does not matter, we can use combinations. We can select 5 batsmen from 7 batsmen in 7C5 ways (21 ways) So, we can complete stage 1 in 21 ways ...” March 29, 2019 Brent@GMATPrepNow posted a reply to What percentage of his bills did Stanley pay before their in the Data Sufficiency forum “Target question: What percentage of his bills did Stanley pay before their due dates last month? This is a great candidate for rephrasing the target question. Aside: We have a free video with tips on rephrasing the target question: Let P = # of bills PAID before due date Let T = TOTAL # of ...” March 29, 2019 Brent@GMATPrepNow posted a reply to If $$n$$ is a positive integer and $$r$$ is the remainder in the Data Sufficiency forum “ Given: r is the remainder when (n² - 1) is divided by 8 Target question: What is the value of r? Statement 1: n is odd Let''s test some ODD values of n If n = 1, then n² - 1 = 1² - 1 = 0, and 0 divided by 8 leaves remainder 0. So, the answer to the target question is r = 0 If n = 3, ...” March 29, 2019 Brent@GMATPrepNow posted a reply to If √k is not an integer, then is k a prime number? in the Data Sufficiency forum “ Given: √k is not an integer Target question: Is k a prime number? Statement 1: k < 10 Let''s TEST some values. There are several values of k that satisfy statement 1. Here are two: Case a: k = 1.3 (√1.3 is not an integer). In this case, the answer to the target question is NO, ...” March 29, 2019 Brent@GMATPrepNow posted a reply to The ratio of boys to girls in Class A is 3 to 4. The ratio in the Problem Solving forum “The ratio of boys to girls in Class A is 3 to 4. Let B = number of boys in class A Let G = number of girls in class A We get: B/G = 3/4 Cross multiply to get: 4B = 3G Class A has one more boy and two more girls than class B So B - 1 = number of boys in class B So G - 2 = number of girls in ...” March 29, 2019 fskilnik@GMATH posted a reply to The graphs of f(x) = x^3-x and g(x) = mx+n are represent in the Problem Solving forum “https://i.postimg.cc/ZnnBXy0K/28-Mar19-4.gif $$? = m \cdot n$$ $$f\left( x \right) = {x^3} - x = x\left( {{x^2} - 1} \right) = x\left( {x + 1} \right)\left( {x - 1} \right)$$ $$f\left( 2 \right) = 6\,\,\,\,\,\, \Rightarrow \,\,\,\,\,A = \left( {2,6} \right)$$ $$f\left( x \right) = 0\,\,\,\, ...” March 28, 2019 fskilnik@GMATH posted a reply to Company ABC has decided to distribute to its clients several in the Problem Solving forum “$$? = N\,\,\,\,\left( {\# \,{\rm{clients}}} \right)\leftGMATH method. Regards, Fabio.” March 28, 2019 fskilnik@GMATH posted a reply to The sum of all integers between 500 and 2500 that are divisi in the Problem Solving forum “$$? = \sum N \,\,\,::\,\,\,\left\{ \matrix{ \,500 < N\,\,{\mathop{\rm int}} < 2500\,\,\,\,\left( * \right) \hfill \cr \,{N \over {2 \cdot {3^2}}} = {\mathop{\rm int}} \,\,\,;\,\,\,{N \over {3 \cdot {5^2}}} = {\mathop{\rm int}} \,\,\,\,\left( {**} \right) \hfill \cr} \right.$$ ...” March 28, 2019 fskilnik@GMATH posted a new topic called The graphs of f(x) = x^3-x and g(x) = mx+n are represent in the Problem Solving forum “GMATH practice exercise (Quant Class 20) The graphs of f(x) = x^3-x and g(x) = mx+n are represented in the figure given. If m and n are constants, what is the value of mn ? https://i.postimg.cc/y8hscxrx/28-Mar19-3z.gif (A) -4 (B) -2 (C) 2 (D) 4 (E) 6 Answer: ______(D)__” March 28, 2019 fskilnik@GMATH posted a new topic called Company ABC has decided to distribute to its clients several in the Problem Solving forum “GMATH practice exercise (Quant Class 17) Company ABC has decided to distribute to its clients several shares of stocks, 1000 stocks per share. Mr. Alicante (its minor client) received 1 share, Mrs. Jung (its second minor client) received 3 shares, Mrs. Thompson (its third minor client) received 5 ...” March 28, 2019 fskilnik@GMATH posted a new topic called The sum of all integers between 500 and 2500 that are divisi in the Problem Solving forum “GMATH practice exercise (Quant Class 16) The sum of all integers between 500 and 2500 that are divisible by both 18 and 75 is: (A) 6750 (B) 6300 (C) 5400 (D) 4050 (E) 3150 Answer: ______(B)__” March 28, 2019 Brent@GMATPrepNow posted a reply to Bite-sized video lessons from GMAT Prep Now in the GMAT Math forum “Data Sufficiency lesson #5: - Summarizing Information Video : https://www.youtube.com/watch?v=cK9PR3SLsSA Cheers, Brent” March 27, 2019 fskilnik@GMATH posted a reply to If x+sqrt(x^2-4x+4)=2, then: in the Problem Solving forum “Important: Have you realized (looking at the alternative choices carefully) that the answer MUST BE (A)? Reason: if (B), (C), (D), or (E) is true, then (A) is also true! On the other hand, the GMAT asks you to find the BEST answer, therefore this approach could be considered ...” March 27, 2019 fskilnik@GMATH posted a new topic called If x+sqrt(x^2-4x+4)=2, then: in the Problem Solving forum “GMATH practice exercise (Quant Class 12) https://i.postimg.cc/jShGfcfw/27-Mar19-3.gif Answer: ______ (A)__ Hint: The alternative choices are tricky... the official answer is NOT wrong... and you can find it in 3 SECONDS, using LOGIC only! Obs.: someone could argue that GMAT asks you to ...” March 27, 2019 Brent@GMATPrepNow posted a reply to The water from one outlet, flowing at a constant rate, can in the Problem Solving forum “So, let''s say that the volume of the pool is 45 gallons. The water from one outlet, flowing at a constant rate, can fill a swimming pool in 9 hours So, this outlet pumps at a rate of 5 gallons per hour The water from a second outlet, flowing at a constant rate, can fill the same pool in 5 ...” March 27, 2019 Brent@GMATPrepNow posted a reply to If a positive integer t is not divisible by 5, how many poss in the Problem Solving forum “Since t is NOT divisible by 5, we need only test t = 1, 2, 3 and 4 If t = 1, then t⁴ = 1, and 1 divided by 5 leaves remainder 1 If t = 2, then t⁴ = 16, and 16 divided by 5 leaves remainder 1 If t = 3, then t⁴ = 81, and 81 divided by 5 leaves remainder 1 If t = 4, then t⁴ = 256, and ...” March 27, 2019 Brent@GMATPrepNow posted a reply to At a certain school, the student to teacher ratio is 52 to 9 in the Problem Solving forum “There''s a nice integer properties rule that says: If j is a multiple of d, and k is NOT a multiple of d, then j-k (and j+k) is NOT a multiple of d For example, since 56 is a multiple of 7, and 11 is NOT a multiple of 7, then 56-11 is NOT a multiple of 7 At a certain school, the student to ...” March 27, 2019 fskilnik@GMATH posted a reply to At a certain school, the student to teacher ratio is 52 to 9 in the Problem Solving forum “$$?\,\,\,:\,\,\,\left( {{\text{final}}\,\,S,{\text{final}}\,\,T} \right)\,\,\,\,\,\underline {{\text{possible}}}$$ $$\left\{ \matrix{ S\,\,:\,\,\,\,52k\,\,\,\,\, \to \,\,\,\,\,52k - 38 \hfill \cr T\,\,:\,\,\,\,9k\,\,\,\,\, \to \,\,\,\,\,9k - 11 \hfill \cr} \right.\,\,\,\,\,\left( {k \ge ...” March 27, 2019 fskilnik@GMATH posted a reply to Two trains travel at constant speeds. What is the ratio of t in the Data Sufficiency forum “$${\rm{faster}}\,\,{\rm{train}}\,\,\left\{ \matrix{ \,x\,\,{\rm{m}}\,\,\left( {{\rm{length}}\,{\rm{:}}\,\,{\rm{meters}}} \right) \hfill \cr \,A\,{\rm{mph}}\,\,\,\left( {{\rm{speed}}\,{\rm{:}}\,\,{\rm{meters}}\,\,{\rm{per}}\,\,{\rm{hour}}} \right) \hfill \cr} \right.$$...” March 26, 2019 fskilnik@GMATH posted a reply to ((x+y+1)/(x+y))((x+z+2)/(x+z))((x+w+3)/(x+w))>8? in the Data Sufficiency forum “$$A = {{\left( {x + y + 1} \right)} \over {x + y}} \cdot {{\left( {x + z + 2} \right)} \over {x + z}} \cdot {{\left( {x + w + 3} \right)} \over {x + w}} = \left( {1 + {1 \over {x + y}}} \right)\left( {1 + {2 \over {x + z}}} \right)\left( {1 + {3 \over {x + w}}} \right)\,\,\,\mathop > \limits^? ...” March 26, 2019 fskilnik@GMATH posted a reply to Last Monday N female executives (N>1) received M male man in the Data Sufficiency forum “$$m,n\,\, \ge \,\,2\,\,\,{\rm{ints}}\,\,\,\,\left( * \right)$$ $$? = C\left( {m + n,2} \right) - C\left( {n,2} \right) = {{\left( {m + n} \right)\left( {m + n - 1} \right)} \over 2} - {{n\left( {n - 1} \right)} \over 2}$$ $$? = \frac{{m\left( {m + n - 1} \right) + nm + n\left( {n - 1} \right) - ...” March 26, 2019 fskilnik@GMATH posted a new topic called Two trains travel at constant speeds. What is the ratio of t in the Data Sufficiency forum “GMATH practice exercise (Quant Class 19) Two trains travel at constant speeds. What is the ratio of the slower speed to the faster speed? (1) The time it takes for one train to pass the other when they are in the same direction is 3h. (2) The time it takes for one train to pass the other ...” March 26, 2019 fskilnik@GMATH posted a new topic called ((x+y+1)/(x+y))((x+z+2)/(x+z))((x+w+3)/(x+w))>8? in the Data Sufficiency forum “GMATH practice exercise (Quant Class 14) https://i.postimg.cc/KjBctDqw/26-Mar19-3w.gif Answer: _____(A)__” March 26, 2019 Brent@GMATPrepNow posted a new topic called At a certain school, the student to teacher ratio is 52 to 9 in the Problem Solving forum “At a certain school, the student to teacher ratio is 52 to 9. If 38 students and 11 teachers leave, which of the following COULD represent the number of students and teachers remaining at the school? A) 532 students and 88 teachers B) 794 students and 162 teachers C) 1106 students and 225 ...” March 26, 2019 fskilnik@GMATH posted a new topic called Last Monday N female executives (N>1) received M male manage in the Data Sufficiency forum “GMATH practice exercise (Quant Class 18) Last Monday N female executives (N>1) received M male managers (M>1) for a business meeting. If every person shook hands exactly once with every other person in the meeting, what is the difference between the total number of shaking hands and the ...” March 26, 2019 Brent@GMATPrepNow posted a reply to For all positive integers m in the Problem Solving forum “Thanks Roach! Cheers, Brent - now with 50% less "t"!!” March 25, 2019 Brent@GMATPrepNow posted a reply to When f(x)=x^3+1/x3, which of the following is equal to f(-1/ in the Problem Solving forum “GIVEN: f(x)=x³ + 1/x³ So, f(-1/x) = (-1/x)³ + 1/(-1/x)³ = -1/x³ + 1/(-1/x³) = -1/x³ - x³ = -(1/x³ + x³) = -(x³ + 1/x³) = -f(x) Answer: B Cheers, Brent” March 25, 2019 Brent@GMATPrepNow posted a reply to Last year a certain bond with a face value of 5,000 yielded in the Problem Solving forum “Last year a certain bond with a face value of 5,000 yielded 8 percent of its face value in interest 8% of 5,000 = 400 So, interest = 400 If that interest was approximately 6.5 percent of the bond''s selling price,approximately what was the bond''s selling price? Let x = the bond''s ...” March 25, 2019 Brent@GMATPrepNow posted a reply to Is it true that x > 0? in the Data Sufficiency forum “Target question: Is it true that x > 0? Statement 1: x² = 2x Rewrite as: x² - 2x = 0 Factor: x(x - 2) = 0 So, EITHER x = 0 OR x = 2 Let''s examine each possible case Case a: If x = 0, then the answer to the target question is NO, it is not true that x > 0 Case b: If x = 2, then ...” March 24, 2019 Brent@GMATPrepNow posted a reply to Problem with a practice question in the GMAT Math forum “Here''s my full solution: https://www.beatthegmat.com/for-all-positive-integers-m-t299496.html Cheers, Brent” March 23, 2019 Brent@GMATPrepNow posted a reply to If $$xy \neq 0$$, and 75 percent of $$x$$ equals 125 percent in the Problem Solving forum “GIVEN: 75 percent of x equals 125 percent of y Rewrite as: 3/4 of x = 5/4 of y Or we can say: (3/4)(x) = (5/4)( y) Multiply both sides by 4 to get: 3x = 5y Divide both sides by 5 to get: 3x/5 = y Rewrite as: y = (3/5)(x) Or y = 3/5 of x Or y = 60/100 of x Or y = 60% of x Answer: C ...” March 22, 2019 Brent@GMATPrepNow posted a reply to If m and n are prime numbers, what is the value of m+n? in the Data Sufficiency forum “ Given: m and n are prime numbers Target question: What is the value of m+n? Statement 1: 15 ≤ m < n ≤ 20 17 and 19 are the only PRIME numbers from 15 to 20 inclusive So, it must be the case that m = 17 and n = 19 So, the answer to the target question is m+n = 17 + 19 = 33 Since ...” March 22, 2019 Brent@GMATPrepNow posted a reply to If n is an integer, is n + 1 odd? in the Data Sufficiency forum “Target question: Is n + 1 odd? Some important rules: #1. ODD +/- ODD = EVEN #2. ODD +/- EVEN = ODD #3. EVEN +/- EVEN = EVEN Statement 1: n + 2 is an even integer. In other words: n + EVEN = EVEN In other words: n = EVEN - EVEN By Rule #3, n must be even, which means n+1 is ODD The ...” March 22, 2019 Brent@GMATPrepNow posted a reply to Express 2^20-2^19-2^18-2^17 as a power of 2. in the Problem Solving forum “2^20 - 2^19 - 2^18 - 2^17 = 2^17(2^3 - 2^2 - 2^1 - 1) = 2^17(8 - 4 - 2 - 1) = 2^17(1) = 2^17 Answer: C Cheers, Brent” March 22, 2019 fskilnik@GMATH posted a reply to The straight lines given by the equation 2x^2=2y^2-3xy are: in the Problem Solving forum “$$?\,\,:\,\,{\rm{lines}}\,\,{\rm{relative}}\,\,{\rm{position}}2{x^2} = 2{y^2} - 3xy\,\,\,\, \Leftrightarrow \,\,\,\,2{x^2} - xy = 2{y^2} - 4xy\,\,\,\, \Leftrightarrow  \Leftrightarrow \,\,\,\,x\left( {2x - y} \right) = - 2y\left( { - y + 2x} \right)\,\,\,\, \Leftrightarrow ...” March 21, 2019 fskilnik@GMATH posted a reply to If (r+1/r)^2 = 5, what is the value of (r^3+1/r^3)^2? in the Problem Solving forum “$${\left( {r + {1 \over r}} \right)^2} = 5\,\,\,\,\,\left( * \right)$$ $$? = {\left( {{r^3} + {1 \over {{r^3}}}} \right)^2}$$ $$?\,\,\, = \,\,\,{\leftGMATH method. Regards, Fabio.” March 21, 2019 fskilnik@GMATH posted a reply to A dessert recipe calls for 50% melted chocolate and 50% in the Problem Solving forum “$$?\,\,\, = \,\,\,x = \# \,\,{\text{out}}\,\,\underline {{\text{sauce}}} \,\,{\text{cups}}\,\, = \,\,\# \,\,{\text{in}}\,\,\underline {{\text{100 % }}\,\,{\text{choco}}} \,\,{\text{cups}}\matrix{ {{\rm{real}} \to {\rm{ideal}}} \cr {15\,\,{\rm{cups}}} \cr } \,\,\,\left\{ ...” March 21, 2019 fskilnik@GMATH posted a new topic called The straight lines given by the equation 2x^2=2y^2-3xy are: in the Problem Solving forum “GMATH practice exercise (Quant Class 20) The straight lines given by the equation 2(x^2)=2(y^2)-3xy are: (A) parallel (B) intersecting and they form a 30-degrees angle (C) intersecting and they form a 45-degrees angle (D) intersecting and they form a 60-degrees angle (E) intersecting and ...” March 21, 2019 fskilnik@GMATH posted a new topic called If (r+1/r)^2 = 5, what is the value of (r^3+1/r^3)^2? in the Problem Solving forum “GMATH practice exercise (Quant Class 3) If (r+1/r)^2 = 5, what is the value of (r^3+1/r^3)^2? (A) 7.75 (B) 10 (C) 12.25 (D) 15 (E) 20 Answer: _____(E)__” March 21, 2019 Brent@GMATPrepNow posted a reply to What is the total cost to make 7 long distance telephone in the Data Sufficiency forum “Target question: What is the total cost to make 7 long distance telephone calls? When we SCAN the statements, we see the key phrase: at least This allows us to jump straight to... Statements 1 and 2 combined There are infinitely many scenarios that satisfy BOTH statements. Here are two: ...” March 21, 2019 Brent@GMATPrepNow posted a reply to Skier Lindsey Vonn completes a straight 300-meter downhill in the Problem Solving forum “The ride up the mountain took 135 seconds longer than her run down the mountain Start with a word equation: (time going UP mountain) = (time going DOWN mountain) + 135 time = distance/speed We can now write: 300/(x - 8) = 300/(x + 10) + 135 Multiply both sides by (x - 8) to get: 300 = 300(x - ...” March 21, 2019 Brent@GMATPrepNow posted a reply to x is the product of all even numbers from 2 to 50, inclusive in the Problem Solving forum “x = (2)(4)(6)....(46)(48)(50) = (1)(2)(2)(2)(3)(2).....(23)(2)(24)(2)(25)(2) Notice that: x is divisible by 2. This tells us that x+1 is 1 greater than a multiple of 2. In other words, x+1 is NOT divisible by 2 x is divisible by 3. This tells us that x+1 is 1 greater than a multiple of 3. ...” March 20, 2019 fskilnik@GMATH posted a reply to xy=? in the Data Sufficiency forum “$$? = xy$$ $$\left( 1 \right)\,\,\,{\left( {x - 2} \right)^2} = - \left| {y - 3} \right|\,\,\,\,\,\left( * \right)$$ $$\left. \matrix{ {\left( {x - 2} \right)^2} \ge 0 \hfill \cr - \left| {y - 3} \right| \le 0\,\, \hfill \cr} \right\}\,\,\,\,\,\mathop \Rightarrow \limits^{\left( * ...” March 20, 2019 fskilnik@GMATH posted a reply to Jeonghee has 5 different red cards and 5 different blue card in the Problem Solving forum “$$? = P\left( {{\rm{red}}\,\,{\rm{together}}\,{\rm{,}}\,{\rm{blue}}\,\,{\rm{together}}} \right){\rm{total}}\,:\,\,\,\underbrace {C\left( {10,5} \right)}_{{\rm{cards}}\,\,{\rm{chosen}}}\,\, \cdot \,\,\underbrace {\,\,5!\,\,}_{{\rm{cards}}\,\,{\rm{chosen}}\,\,{\rm{order}}}\,\,\,\, = \,\,\,{{10 ...” March 20, 2019 Brent@GMATPrepNow posted a reply to If there are 4 pairs of twins, and a committee will be in the Problem Solving forum “Here''s one approach. Take the task of selecting the 3 committee members and break it into stages. Stage 1: Select the 3 twins from which we will select 1 spouse each. There are 4 sets of twins, and we must select 3 of them. Since the order in which we select the 3 twins does not matter, ...” March 20, 2019 Brent@GMATPrepNow posted a reply to If arc PQR above is a semicircle, what is the length of diam in the Data Sufficiency forum “http://s16.postimg.cc/p2mwbwdpt/triangle_PQR.jpg We can answer this question without performing any calculations. Instead, we can use some visualization. Important point: For geometry DS questions, we are typically checking to see whether the statements "lock" a particular angle or ...” March 20, 2019 Brent@GMATPrepNow posted a reply to In a group of children, the average (arithmetic mean) weight in the Problem Solving forum “We can also use weighted averages to solve this Weighted average of groups combined = (group A proportion)(group A average) + (group B proportion)(group B average) + (group C proportion)(group C average) + ... Let G = number of girls Let B = number of boys So, G+B = TOTAL number of children ...” March 20, 2019 Brent@GMATPrepNow posted a reply to If the average (arithmetic mean) of five consecutive negativ in the Problem Solving forum “Let x = the 1st (smallest integer) So, x+1 = the 2nd integer x+2 = the 3rd integer x+3 = the 4th integer x+4 = the 5th integer (greatest integer) What is the difference between the greatest and least of the five integers? Difference = ( x+4) - x = 4 Answer: A Cheers, Brent” March 19, 2019 Brent@GMATPrepNow posted a reply to The number 1000 lies between two consecutive perfect squares in the Problem Solving forum “Let''s examine some perfect squares that are close to 1000 30² = 900 31² = 961 32² = 1024 So, 1000 lies between 961 (aka 31²) and 1024 (aka 32²) 1000 is closer to 1024 (aka 32²) than to 961 Answer: D Cheers, Brent” March 19, 2019 Brent@GMATPrepNow posted a reply to Danny spends$360 buying his favorite dolls. If he buy only in the Problem Solving forum
“Let L = cost of 1 LARGE LemonHead doll So L-1 = cost of 1 SMALL LemonHead doll If he buys only small LemonHead dolls, which are $1 cheaper than the large LemonHead dolls, he could buy 5 more dolls than if he were to buy only large LemonHead dolls. Let''s first write a "word equation": ...” March 18, 2019 fskilnik@GMATH posted a reply to If 5 is approximately equal to 2^(2.322), which of the follo in the Problem Solving forum “$${2^{2.322}} \cong 5\,\,\,\, \Rightarrow \,\,\,\,\,{\left( {{2^{2.322}}} \right)^{0.5}} = {5^{0.5}}\left( * \right)$$ $${{{2^{ - 5}} \cdot \root 3 \of {{{10}^2}} } \over {\root 6 \of {10} \cdot {2^x}}} = 1\,\,\,\, \Rightarrow \,\,\,{{\root 3 \of {{{10}^2}} } \over {\root 6 \of {10} }} = {{{2^x}} ...” March 18, 2019 fskilnik@GMATH posted a reply to There are many boxes in a certain room, and each box has a l in the Problem Solving forum “$$4 \cdot 1 + 4 \cdot 2 + \ldots + 4 \cdot N = 612? = N\,\,\,\,\left( {N \ge 1\,\,{\mathop{\rm int}} } \right)\,\,\,\left( * \right)612 = 4(1 + 2 + \ldots + N)\,\,\,\mathop = \limits^{{\rm{Arith}}{\rm{.Seq}}} \,\,\,4\leftGMATH method. Regards, Fabio.” March 18, 2019 fskilnik@GMATH posted a reply to If A>B are two odd numbers, how many even numbers are the in the Problem Solving forum “$$?\,\, = \,\,\# \,\,{\rm{even}}\,\,{\rm{numbers}}\,\,{\rm{in}}\,\,\leftSecond Approach ("the technical way"):$$? = \# \,\,{\rm{even}}\,\,{\rm{numbers}}\,\,{\rm{in}}\,\,I = \leftGMATH method. Regards, Fabio.” March 18, 2019 fskilnik@GMATH posted a reply to If A>B are two odd numbers, how many even numbers are the in the Problem Solving forum “$$?\,\, = \,\,\# \,\,{\rm{even}}\,\,{\rm{numbers}}\,\,{\rm{in}}\,\,\leftFirst Approach ("the smart way"):$${\rm{Take}}\,\,\left( {B,A} \right) = \left( {1,5} \right)\,\,\,\,\, \Rightarrow \,\,\,\,\,{\rm{Target}} = 2\,\,\,\,\,\leftGMATH method. Regards, Fabio.” March 18, 2019 fskilnik@GMATH posted a reply to If f is a function defined for every positive integer x in s in the Problem Solving forum “$${x^2} \cdot f\left( x \right) = {2^{8 - x}}\,\,\,\,\left( * \right)$$ $$? = 100 \cdot f\left( 5 \right)$$ $$x = 5\,\,\,\,\,\mathop \Rightarrow \limits^{\left( * \right)} \,\,\,\,\,25 \cdot f\left( 5 \right) = {2^3}\,\,\,\,\mathop \Rightarrow \limits^{ \cdot \,\,4} \,\,\,\,? = 4 \cdot {2^3} = ...” March 18, 2019 fskilnik@GMATH posted a new topic called There are many boxes in a certain room, and each box has a l in the Problem Solving forum “GMATH practice exercise (Quant Class 17) There are many boxes in a certain room, and each box has a label attached to it in which the number of balls contained in that box is written. If there are exactly 612 balls in all boxes combined, and it is known that the numbers presented at the labels ...” March 17, 2019 fskilnik@GMATH posted a new topic called If A>B are two odd numbers, how many even numbers are there in the Problem Solving forum “GMATH practice exercise (Quant Class 16) If A>B are two odd numbers, how many even numbers are there between them? (A) (A+B)/2 (B) A-B+1 (C) A-B (D) A-B-1 (E) (A-B)/2 Answer: _____(E)__ ” March 17, 2019 fskilnik@GMATH posted a new topic called If f is a function defined for every positive integer x in s in the Problem Solving forum “GMATH practice exercise (Quant Class 3) https://i.postimg.cc/SsDKwW9r/17-Mar19-6y.gif Answer: _____(C)__” March 17, 2019 fskilnik@GMATH posted a new topic called If 5 is approximately equal to 2^(2.322), which of the follo in the Problem Solving forum “GMATH practice exercise (Quant Class 12) https://i.postimg.cc/cJzYVGNC/17-Mar19-3g.gif Answer: _____(B)___” March 17, 2019 fskilnik@GMATH posted a reply to If quadrilaterals ABCD and ADEF have the same areas, is AF&a in the Data Sufficiency forum “https://i.postimg.cc/fTD6f9kR/15-Mar19-10q.gif$${S_{{\mathop{\rm ABCD}\nolimits} }} = {S_{{\rm{ADEF}}}} = {S_{{\rm{ADEG}}}} + {S_{{\rm{AGF}}}}\,\,\,\,\,\left( * \right)AF\,\,\mathop > \limits^? \,\,28\left( 1 \right)\,\,\left\{ \matrix{ \,{\rm{image}}\,\,{\rm{left}}:\,\,\left( ...” March 17, 2019 Brent@GMATPrepNow posted a reply to Bea owns how many more CDs than Al owns? (1) If Bea gives 9 in the Data Sufficiency forum “Let A = number of CDs Al owns Let B = number of CDs Bea owns Target question: What is the value of B - A? Statement 1: If Bea gives 9 of her CDs to Al, then Al will own twice as many CDs as Bea owns. We can create the equation: 2(B - 9) = A+9 Expand left side to get 2B - 18 = A+9 ...” March 16, 2019 Brent@GMATPrepNow posted a reply to How many different 3-digit numbers are greater than 299 and in the Problem Solving forum “Take the task of creating the 3-digit numbers and break it into stages. Stage 1: Select the first digit (hundreds digit) Since the first digit can be 3, 4, 5, 7 or 9, we can complete stage 1 in 5 ways Stage 2: Select the second digit (tens digit) Since the second digit can be 0, 2, 3, 4, ...” March 15, 2019 fskilnik@GMATH posted a new topic called If quadrilaterals ABCD and ADEF have the same areas, is AF>2 in the Data Sufficiency forum “GMATH practice exercise (Quant Class 15) https://i.postimg.cc/hGP6RWVW/15-Mar19-3w.gif If quadrilaterals ABCD and ADEF have the same areas, is AF > 28 ? (1) EF = 10 (2) CE = 24 Answer: ______(C)__ ” March 15, 2019 Brent@GMATPrepNow posted a reply to The cost of delivery for an order of desk chairs was$10.00 in the Data Sufficiency forum
“Target question: Is n > 24? Given: The cost of delivery for an order of desk chairs was $10.00 for the 1st chair, and$1 for each additional chair in the order. The office manager placed an order for n desk chairs. Statement 1: The delivery cost for the order totaled more than $30.00 ...” March 15, 2019 Brent@GMATPrepNow posted a reply to What is the average (arithmetic mean) of eleven consecutive in the Data Sufficiency forum “There''s a nice rule that says, "In a set where the numbers are equally spaced, the mean will equal the median." Since the consecutive integers are equally-spaced, their mean and median will be equal. Target question: What is the average of eleven consecutive integers? ...” March 15, 2019 Brent@GMATPrepNow posted a reply to If 320 people attended the wedding and 200 attendees drank in the Data Sufficiency forum “This question is somewhat ambiguous, since it''s hard to say whether "nondrinkers" in statement 1 refers to people who drank neither beer nor wine, or did not drink beer. I''m assuming that it means to not drink beer, so I''ve add that to the question below. One approach is to use ...” March 14, 2019 Brent@GMATPrepNow posted a reply to Set X consists of different positive numbers arranged in in the Data Sufficiency forum “Target question: What is the arithmetic mean of set X? Given: Set X consists of different positive numbers arranged in ascending order: K, L, M, 5, 7. K, L and M are consecutive integers This means that EITHER K, L, M = 1, 2, 3 respectively, OR K, L, M = 2, 3, 4 respectively Head straight ...” March 14, 2019 fskilnik@GMATH posted a reply to If N is a positive two-digit integer, is N+1 prime? in the Data Sufficiency forum “Thank you both (Mitch and Ian) for your nice contributions! $$N = \left\langle {AB} \right\rangle$$ $$N + 1\,\,\mathop = \limits^? \,\,{\rm{prime}}$$ $$\left( 1 \right)\,\,A + B = 11\,\,\,\,\left\{ \matrix{ \,B\,\,{\rm{odd}}\,\,\,\, \Rightarrow \,\,\,\left\langle {{\rm{NO}}} \right\rangle ...” March 14, 2019 fskilnik@GMATH posted a reply to What is the selling price (in dollars) of the HK11B-connecto in the Data Sufficiency forum “$$s,c\,\,\, \to \,\,\,\,\leftGMATH method. Regards, Fabio.” March 14, 2019 fskilnik@GMATH posted a new topic called If N is a positive two-digit integer, is N+1 prime? in the Data Sufficiency forum “GMATH practice exercise (Quant Class 16) If N is a positive two-digit integer, is N+1 prime? (1) The sum of the digits of N is equal to 11. (2) N-1 is divisible by 7. Answer: _____(A)__” March 14, 2019 fskilnik@GMATH posted a new topic called What is the selling price (in dollars) of the HK11B-connecto in the Data Sufficiency forum “GMATH practice exercise (Quant Class 14) What is the selling price (in dollars) of the HK11B-connector (a specific electronic widget) in Mrs. Tao´s store? (1) In Mrs. Tao´s store, the difference between the selling price of the HK11B-connector and the cost of this electronic widget is 500 ...” March 14, 2019 fskilnik@GMATH posted a reply to If c is a nonzero constant such that x*f(x) = c, variables x in the Problem Solving forum “https://i.postimg.cc/258f4wYr/13-Mar19-8w.gif $$? = c = {1 \over 2} \cdot b\,\,\,\,\,\,\leftGMATH method. Regards, Fabio.” March 13, 2019 fskilnik@GMATH posted a reply to An airplane leaves city A to make a connection in city C, be in the Problem Solving forum “https://i.postimg.cc/fbknkfmF/13-Mar19-4g.gif$$?\,\,\, \cong \,\,\,AC + CB\,\,\,\,\leftGMATH method. Regards, Fabio.” March 13, 2019 Brent@GMATPrepNow posted a reply to combinations in the Problem Solving forum “Sure thing. Number of outcomes that OBEY the restriction = (total # of outcomes that IGNORE the restriction) - (# of outcomes that BREAK the restriction) total # of outcomes that IGNORE the restriction Select any 3 people from the 8 people We can do this in 8C3 ways (= 56 ways) # of ...” March 13, 2019 fskilnik@GMATH posted a reply to The number of candidates rejected in a certain admission pro in the Problem Solving forum “$$?\,\,\,:\,\,\,{\rm{total}}\,\,{\rm{\# }}\,\,\,\left( {{\rm{possible}}\,\,{\rm{value}}} \right)$$ $$\left\{ \matrix{ \,{\rm{accepted}} = k \hfill \cr \,{\rm{rejected}} = 5k \hfill \cr} \right.\,\,\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,? = 6k\,\,\,\,\,\,\left( {k \ge 1\,\,{\mathop{\rm ...” March 13, 2019 Brent@GMATPrepNow posted a reply to If when x is divided by z, the result is y remainder q, then in the Problem Solving forum “When it comes to remainders, there''s a nice rule that says, "If N divided by D equals Q with remainder R, then N = DQ + R" For example, since 17 divided by 5 equals 3 with remainder 2, then we can write 17 = (5)(3) + 2 Likewise, since 53 divided by 10 equals 5 with remainder 3, then we ...” March 13, 2019 Brent@GMATPrepNow posted a reply to If 5,000 invested for one year at p percent simple annual i in the Data Sufficiency forum “The great thing about DS questions is that we aren''t required to perform calculations if we know that we COULD perform those calculations. Here''s what I mean: Target question: What amount must be invested at k percent simple annual interest for one year to yield the same amount of dollars ? ...” March 13, 2019 Brent@GMATPrepNow posted a reply to If xyz ≠ 0, is x^3y^4z^5 > 0? in the Data Sufficiency forum “ Given: xyz ≠ 0 Target question: Is x³y⁴z⁵ > 0? This is a great candidate for rephrasing the target question. Since we know that x² must be POSITIVE, we can safely take the inequality x³y⁴z⁵ > 0 and divide both sides by x² to get: xy⁴z⁵ > 0 Similarly, since ...” March 13, 2019 Brent@GMATPrepNow posted a reply to Set M is composed of the positive even integers up to 100. in the Problem Solving forum “Set M is composed of the positive even integers up to 100. Set M = {2, 4, 6, 8, . . . . 96, 98, 100} Set N is composed of the odd integers from –1 to 99 Set N = {-1, 1, 3, 5, . . . 95, 97, 99} What is the value of (the sum of Set M) – (the sum of Set N)? SUM of set M = 2 + 4 + 6 + 8 + ...” March 13, 2019 fskilnik@GMATH posted a new topic called If c is a nonzero constant such that x*f(x) = c, variables x in the Problem Solving forum “GMATH practice exercise (Quant Class 20) https://i.postimg.cc/8cxcjYfy/13-Mar19-7z.gif If c is a nonzero constant such that x*f(x) = c, variables x and y=f(x) are said to be inversely proportional. If the dotted curve shown above, defined by the points (x,y) where x>0 and y=f(x), represents ...” March 13, 2019 Brent@GMATPrepNow posted a reply to A certain ball was dropped from a window 8 meters above a in the Problem Solving forum “Drop 8 meters Rise 4 meters Drop 4 meters Rise 2 meters Drop 2 meters Rise 1 meters (DONE!) 8 + 4 + 4 + 2 + 2 + 1 = 21 meters Answer: A Cheers, Brent” March 13, 2019 fskilnik@GMATH posted a new topic called An airplane leaves city A to make a connection in city C, be in the Problem Solving forum “GMATH practice exercise (Quant Class 2) https://i.postimg.cc/J7NbScJb/13-Mar19-3w.gif An airplane leaves city A to make a connection in city C, before going on to city B (as shown in the map). If the map scale is 1cm=100km, which of the following is closest to the minimum possible distance ...” March 13, 2019 Brent@GMATPrepNow posted a reply to A certain hotel has 1,400 single rooms and 420 double rooms. in the Problem Solving forum “The hotel has 1,400 single rooms, and one person can clean a single room every 15 minutes So, one person can clean 4 single rooms in ONE HOUR In other words, it takes 1 WORKER HOUR to clean 4 single rooms 1400/4 = 350 So, it takes 350 WORKER HOURS to clean 1400 rooms The hotel has 420 ...” March 13, 2019 Brent@GMATPrepNow posted a reply to The number of candidates rejected in a certain admission pro in the Problem Solving forum “The number of candidates rejected in a certain admission process was four times GREATER than the number of candidates accepted. Let x = the number of candidates accepted So, x + 4x = the number of candidates rejected In other words, 5x = the number of candidates rejected So, 6x = TOTAL number ...” March 13, 2019 fskilnik@GMATH posted a new topic called The number of candidates rejected in a certain admission pro in the Problem Solving forum “GMATH practice exercise (Quant Class 6) The number of candidates rejected in a certain admission process was four times greater than the number of candidates accepted. Which of the following could be the total number of candidates that applied for this admission process? (A) 726 (B) 727 (C) ...” March 13, 2019 fskilnik@GMATH posted a reply to Which of the following could be the number of diagonals of a in the Problem Solving forum “Let´s connect Mitch´s nice argument with mine (above):$$d = C\left( {N,2} \right) - N = {{N!} \over {2!\left( {N - 2} \right)!}} - N = {{N\left( {N - 1} \right)} \over 2} - {{2N} \over 2} = {{N\left( {N - 3} \right)} \over 2}$$Regards, Fabio.” March 12, 2019 fskilnik@GMATH posted a reply to Which of the following could be the number of diagonals of a in the Problem Solving forum “$$?\,\,\,:\,\,\,\# \,d\,\,\underline {{\rm{could}}\,\,{\rm{be}}} \,\,\,\,\left( {N \ge 3\,\,{\mathop{\rm int}} \,\,\left( * \right)\,,\,\,N{\rm{ - polygon}}} \right)d\,\, \to \,\,\,\left\{ \matrix{ \,{\rm{each}}\,\,{\rm{vertex}}\,\,{\rm{with}}\,\,\left( {{\rm{not}}\,\,{\rm{itself}}} ...” March 12, 2019 fskilnik@GMATH posted a reply to Claudio wants to be well prepared for a long marathon that w in the Problem Solving forum “$$?\,\,\,:\,\,\,\min \,N\,\,{\rm{for}}\,\,{\rm{sum}}\,\,\, \ge \,\,\,1800\,$$ $$\left. \matrix{ {a_1} = 15 \hfill \cr {a_2} = 15 + 1 \cdot {1 \over 2} \hfill \cr {a_3} = 15 + 2 \cdot {1 \over 2} \hfill \cr \vdots \hfill \cr {a_N} = 15 + \left( {N - 1} \right) \cdot {1 \over ...” March 12, 2019 fskilnik@GMATH posted a reply to If c is a constant such that the system of equations given a in the Problem Solving forum “$$?\,\,\,:\,\,\,c\,\,\,{\rm{for}}\,\,{\rm{unique}}\,\,{\rm{solution}}\,\,\left( {x,y} \right)c = 0\,\,\,\, \Rightarrow \,\,\,\,\left\{ \matrix{ \,x = 1 \hfill \cr \, - 4y = 0 \hfill \cr} \right.\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\left( {x,y} \right) = \left( {1,0} ...” March 12, 2019 fskilnik@GMATH posted a new topic called If c is a constant such that the system of equations given a in the Problem Solving forum “GMATH practice exercise (Quant Class 10) https://i.postimg.cc/qB8ZZCpW/12-Mar19-3w.gif Answer: _____(E)__” March 12, 2019 fskilnik@GMATH posted a new topic called Claudio wants to be well prepared for a long marathon that w in the Problem Solving forum “GMATH practice exercise (Quant Class 17) Claudio wants to be well prepared for a long marathon that will occur in the near future. His running coach has decided that the training sessions must be done once every two days, starting with a 15-kilometer distance route, and adding exactly 500 ...” March 12, 2019 Brent@GMATPrepNow posted a reply to In a group of 24 musicians, some are pianists and the rest a in the Problem Solving forum “In a group of 24 musicians, some are pianists and the rest are violinists. Let x = number of pianists So, 24-x = number of violinists Exactly 1/2 of the pianists and exactly 2/3 of the violinists belong to a union. So, the number of pianists in the union = x/2 And the number of violinists in ...” March 12, 2019 fskilnik@GMATH posted a reply to If x>0, what is the sum of the roots of the equation x^sq in the Problem Solving forum “$$x > 0\,\,,\,\,\,\,{x^{\sqrt x }} = {x^2}\,\,\,\left( * \right)$$ $$?\,\,:\,\,{\rm{sum}}\,\,{\rm{of}}\,\,{\rm{roots}}$$ $$x = 1\,\,\,\,\,\mathop \Rightarrow \limits^{{\rm{inspection}}} \,\,\,\,\left\{ \matrix{ \,\,{x^{\sqrt x }} = {1^{\sqrt 1 }} = 1 \hfill \cr \,\,{x^2} = {1^2} = 1 ...” March 11, 2019 fskilnik@GMATH posted a reply to What is the ordinate (y-coordinate) of point C? in the Data Sufficiency forum “$$? = {y_C}$$https://i.postimg.cc/sxr9WGzd/11-Mar19-7v.gif$$\left( {1 + 2} \right)\,\,\,\left\{ \matrix{ \,OD = 2\sqrt 2 \hfill \cr \Delta AOB\,\,{\rm{isosceles}} \hfill \cr} \right.\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\left\{ \matrix{ \,\Delta ODB\,\,{\rm{isosceles}} \hfill \cr ...” March 11, 2019 Brent@GMATPrepNow posted a reply to Carmen currently works 30 hours per week at her part-time jo in the Data Sufficiency forum “ Given: Carmen currently works 30 hours per week Target question: If Carmen''s gross hourly wage were to increase by$1.50, how many fewer hours could she work per week and still earn the same gross weekly pay as before the increase? This is a good candidate for rephrasing the target ...”
March 11, 2019
Brent@GMATPrepNow posted a reply to W, X, Y and Z are four different positive integers. When X in the Problem Solving forum
“ Given: When X is divided by Y, the quotient is Z and the remainder is W. ------ASIDE------- There''s a nice rule that says, "If N divided by D equals Q with remainder R, then N = DQ + R" For example, since 17 divided by 5 equals 3 with remainder 2, then we can write 17 = (5)(3) + 2 ...”
March 11, 2019
fskilnik@GMATH posted a new topic called If x>0, what is the sum of the roots of the equation x^sqrt( in the Problem Solving forum
“GMATH practice exercise (Quant Class 12) https://i.postimg.cc/T3Jw2y75/11-Mar19-8k.gif Answer: _____(E)__”
March 11, 2019
fskilnik@GMATH posted a new topic called What is the ordinate (y-coordinate) of point C? in the Data Sufficiency forum
“GMATH practice exercise (Quant Class 20) https://i.postimg.cc/pXvnJtFv/11-Mar19-6j.gif Answer: _____(C)__”
March 11, 2019
fskilnik@GMATH posted a reply to Is (x^2-7x+12)(x^2-5x-14) > 0 ? in the Data Sufficiency forum
“$$\left( {x - 3} \right)\left( {x - 4} \right)\left( {x + 2} \right)\left( {x - 7} \right)\,\,\mathop > \limits^? \,\,0$$ $$\left( 1 \right)\,\,x > 0\,\,\,\left\{ \matrix{ \,{\rm{Take}}\,\,x = 3\,\,\,\, \Rightarrow \,\,\,\left( {x - 3} \right)\left( {x - 4} \right)\left( {x + 2} ...” March 10, 2019 fskilnik@GMATH posted a reply to If (x-1)/(x-3)>(x-2)/(x-4) is equivalent to a<x<b, in the Problem Solving forum “https://i.postimg.cc/QMJ6zv72/10-Mar19-8p.gif Regards, Fabio. ” March 10, 2019 fskilnik@GMATH posted a reply to If (x-1)/(x-3)>(x-2)/(x-4) is equivalent to a<x<b, in the Problem Solving forum “https://i.postimg.cc/qq5DLnKg/10-Mar19-7w.gif The correct answer is (D). We follow the notations and rationale taught in the GMATH method. Regards, Fabio.” March 10, 2019 fskilnik@GMATH posted a reply to If F is a function defined in the positive integers, such th in the Data Sufficiency forum “$$F\left( k \right) \ge 1\,\,{\mathop{\rm int}} \,\,\,\,{\rm{for}}\,\,{\rm{each}}\,\,\,k \ge 1\,\,\,\,\left( * \right)? = F\left( 8 \right)\left( 1 \right)\,\,F\left( {n + 1} \right) = \left( {n + 1} \right) \cdot F\left( n \right)\,\,\,{\rm{for}}\,{\rm{each}}\,\,\,n \ge ...”
March 10, 2019
fskilnik@GMATH posted a new topic called Is (x^2-7x+12)(x^2-5x-14) > 0 ? in the Data Sufficiency forum
“GMATH practice exercise (Quant Class 14) Is (x^2-7x+12)(x^2-5x-14) > 0 ? (1) x > 0 (2) 3 < |x| < 4 Answer: _____(B)__”
March 10, 2019
Brent@GMATPrepNow posted a reply to What is the hundredths digit of the decimal z? in the Data Sufficiency forum
“Target question: What is the hundredths digit of the decimal z? Statement 1: The tenths digit of 100z is 2 Notice what happens when we take a decimal like 0.123456 and multiply it by 100. We get 12.345 (the tenths digit is 3) In the original decimal, the 3 was in the thousandths place. ...”
March 10, 2019
Brent@GMATPrepNow posted a new topic called W, X, Y and Z are four different positive integers. When X in the Problem Solving forum
“W, X, Y and Z are four different positive integers. When X is divided by Y, the quotient is Z and the remainder is W. If W = X – 7, what is the sum of all possible values of W? A) 19 B) 20 C) 21 D) 22 E) 23 Source: www.gmatprepnow.com Difficulty level: 650 - 700”
March 10, 2019
Brent@GMATPrepNow posted a reply to If 4x − 3y = 13 and 5x + 2y = − 1, then x = in the Problem Solving forum
“GIVEN: 4x − 3y = 13 5x + 2y = − 1 Take the TOP equation and multiply both sides by 2 Take the BOTTOM equation and multiply both sides by 3 We get: 8x - 6y = 26 15x + 6y = -3 ADD the two equations to get: 23x = 23 Solve: x = 23/23 = 1 Answer: C Cheers, Brent”
March 10, 2019
fskilnik@GMATH posted a new topic called If (x-1)/(x-3)>(x-2)/(x-4), then a<x<b, where: in the Problem Solving forum
“GMATH practice exercise (Quant Class 11) https://i.postimg.cc/ZKH5VMYt/10-Mar19-6w.gif Answer: _____(D)__”
March 10, 2019
fskilnik@GMATH posted a new topic called If F is a function defined in the positive integers, such th in the Data Sufficiency forum
“GMATH practice exercise (Quant Class 14) If F is a function defined in the positive integers, such that F(k) is a positive integer for each positive integer k, what is the value of F(8)? (1) F(n+1) = (n+1)*F(n), for every positive integer n. (2) F(1)*F(1) = F(1) Answer: _____(C)__”
March 10, 2019
fskilnik@GMATH posted a reply to If 0.845 is an approximate solution for the equation 10^x = in the Problem Solving forum
“$${10^{0.845}} \cong 7$$ $${7^{x + 2}} = 70$$ $$?\,\, \cong x\,\,\,\,\,\,$$ $${7^{x + 2}} = 7 \cdot 10\,\,\,\,\, \Rightarrow \,\,\,\,\,{7^{x + 1}} = 10\,\,\,\,\, \Rightarrow \,\,\,\,\,{\left( {{7^{x + 1}}} \right)^{0.845}} = {10^{0.845}}\,\, \cong \,\,\,7$$ $${7^{0.845\left( {x + 1} \right)}} ...” March 8, 2019 fskilnik@GMATH posted a reply to If the raining season in Jerusalem begins, Dora estimates a in the Problem Solving forum “$$? = P\left( {{\rm{Dora}}\,\,{\rm{travels}}} \right)P\left( {{\rm{season}}\,\,{\rm{raining}}} \right) = 70\% \,\,\,\,\,\, \Rightarrow \,\,\,\,\,P\left( {{\rm{not}}\,\,{\rm{season}}\,\,{\rm{raining}}} \right) = 30\% 20\% \,\,\mathop \to \limits^{\, + \,250\% } \,\,\,\underbrace {60\% + ...”
March 8, 2019
Brent@GMATPrepNow posted a reply to W, X, Y and Z are four different positive integers. in the Data Sufficiency forum
“Target question: What is the value of Z? Given: When X is divided by Y, the quotient is Z and the remainder is W. ------ASIDE------- There''s a nice rule that says, "If N divided by D equals Q with remainder R, then N = DQ + R" For example, since 17 divided by 5 equals 3 with ...”
March 8, 2019
fskilnik@GMATH posted a new topic called If 0.845 is an approximate solution for the equation 10^x = in the Problem Solving forum
“GMATH practice exercise (Quant Class 3) If 0.845 is an approximate solution for the equation 10^x = 7, which of the following fractions is closest to the solution of 7^(x+2) = 70? (A) 29/211 (B) 19/107 (C) 31/169 (D) 43/211 (E) 53/211 Answer: _____(C)__”
March 8, 2019
fskilnik@GMATH posted a new topic called If the raining season in Jerusalem begins, Dora estimates a in the Problem Solving forum
“GMATH practice exercise (Quant Class 19) If the raining season in Jerusalem begins, Dora estimates a 20% probability of traveling to Israel next holidays. If it doesn´t, she guesses her probability of taking this trip is 250% higher. Based on these assumptions, what are Dora´s chances of ...”
March 8, 2019
fskilnik@GMATH posted a reply to What percent of the area of the rhombus ABCD is the area of in the Data Sufficiency forum
“https://i.postimg.cc/RZ2d0s7n/08-Mar19-2x.gif $$? = {{{S_{{\rm{circle}}}}} \over {{S_{{\rm{rhombus}}}}}}$$ $$\left( 1 \right)\,\,\,\left\{ \matrix{ BCD = {60^ \circ } \hfill \cr ABCD\,\,{\rm{rhombus}} \hfill \cr} \right.\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\Delta ...” March 8, 2019 fskilnik@GMATH posted a reply to If 0.02 < x < 0.04 and 100 < y < 250, which of t in the Problem Solving forum “$$?\,\,\,:\,\,\,\frac{{y - x}}{{xy}} = \frac{1}{x} - \frac{1}{y}\,\,\,\,\,\underline {{\text{could}}\,\,{\text{be}}} {2 \over {100}} < x < {4 \over {100}}\,\,\,\,\, \Rightarrow \,\,\,\,\,25 = {{100} \over 4} < {1 \over x} < {{100} \over 2} = 50\,\,\,\,\left( {\rm{I}} \right)$$...” March 8, 2019 fskilnik@GMATH posted a new topic called What percent of the area of the rhombus ABCD is the area of in the Data Sufficiency forum “GMATH practice exercise (Quant Class 19) https://i.postimg.cc/Kv2v8SQL/07-Mar19-7h.gif What percent of the area of the rhombus ABCD is the area of the circle that is inscribed in it? (1) Angle BCD is equal to 60 degrees (2) AB = 4 Answer: _____(A)__ ” March 7, 2019 fskilnik@GMATH posted a reply to W, X, Y and Z are four different positive integers. in the Data Sufficiency forum “Beautiful problem, Brent. Congrats!$$W,X,Y,Z\,\,\, \ge 1\,\,\,{\rm{different}}\,\,{\rm{ints}}\,\,\left( * \right)\left\{ \matrix{ X = ZY + W\,\,,\,\,\,W < Y\,\,\,\left( {**} \right) \hfill \cr \left( * \right)\,\,\,1 \le W < Y\,\,\, \Rightarrow \,\,\,Y \ge 2\,\,\,\left( {***} ...”
March 7, 2019
Brent@GMATPrepNow posted a reply to OG 2017 Ratio Question in the Data Sufficiency forum
“Target question: What is the total number of articles of clothing in the closet? Given: The ratio of the number of shirts to the number of dresses to the number of jackets in the closet is 9:4:5, respectively. If shirts : dresses : jackets = 9 : 4 : 5, then there are infinitely many ...”
March 7, 2019
fskilnik@GMATH posted a reply to Little Julia created a 5-digit integer choosing 5 distinct c in the Problem Solving forum
“$$?\,\, = \,\,{1 \over {\# \,\,{\rm{favorable}}\,\,{\rm{sequences}}}}$$ $${?_{temp}}\,\,\, = \,\,\,\# \,\,{\rm{favorable}}\,\,{\rm{sequences}}$$ $$\left\{ \matrix{ \,{\rm{3}}\,{\rm{central}}\,{\rm{digits}}\,{\rm{are}}\,\,{\rm{1,3,5}}\,\,\,\, \Rightarrow \,\,\,{{\rm{P}}_{\rm{3}}} = ...” March 7, 2019 Brent@GMATPrepNow posted a new topic called W, X, Y and Z are four different positive integers. in the Data Sufficiency forum “W, X, Y and Z are four different positive integers. When X is divided by Y, the quotient is Z and the remainder is W. What is the value of Z? 1) W = X – 4 2) W + Z = 4 Difficulty level: 650 – 700 Source: www.gmatprepnow.com” March 7, 2019 Brent@GMATPrepNow posted a reply to 60 DAY STUDY GUIDE ENQUIRY in the Ask a GMAT Prep Now representative forum “Sorry, but there are no plans to update the 60-day guide in the near future. Cheers, Brent” March 7, 2019 fskilnik@GMATH posted a reply to In the figure shown, all angles are measured in degrees. Wha in the Problem Solving forum “https://i.postimg.cc/ZR8PpLSq/07-Mar19-6r.gif$$? = k\,\,\,\leftGMATH method. Regards, Fabio.”
March 7, 2019
fskilnik@GMATH posted a new topic called Little Julia created a 5-digit integer choosing 5 distinct c in the Problem Solving forum
“GMATH practice exercise (Quant Class 18) https://i.postimg.cc/0QtN8gvh/07-Mar19-4u.gif Little Julia created a 5-digit integer choosing 5 distinct chips, one by one, among the 7 given ones shown above. "Can you do it in such a way that the three central digits add up to 9?", asked ...”
March 7, 2019
fskilnik@GMATH posted a reply to A certain Formula 1 car fuel consumption is 2.5 liters per k in the Problem Solving forum
“$$?\,\,\, = \,\,\,\max \,\,{\rm{laps}}\,\,\,\left( {{\rm{between}}\,\,{\rm{pit - stops}}} \right)$$ $$3.5\,\,{\rm{km}}\,\,\,\, \leftrightarrow \,\,\,\,{\rm{1}}\,\,{\rm{lap}}\,\,\,\,\,$$ $${\rm{consumption}}\,\,:\,\,2.5\,\,{\rm{liters}}\,\,\,\, \leftrightarrow \,\,\,\,{\rm{1}}\,\,{\rm{km}}$$ ...”
March 7, 2019
fskilnik@GMATH posted a new topic called In the figure shown, all angles are measured in degrees. Wha in the Problem Solving forum
“GMATH practice exercise (Quant Class 1) https://i.postimg.cc/CL0hnHMc/07-Mar19-5c.gif In the figure shown, lines m and n are parallel and all angles are measured in degrees. What is the value of k? (A) 18 (B) 20 (C) 22 (D) 25 (E) 27 Answer: _____(B)__”
March 7, 2019
fskilnik@GMATH posted a new topic called A certain Formula 1 car fuel consumption is 2.5 liters per k in the Problem Solving forum
“GMATH practice exercise (Quant Class 5) A certain Formula 1 car fuel consumption is 2.5 liters per kilometer, and the supply pump injects 11 liters of fuel per second. Every time a pit stop for refueling is needed (i.e., the fuel tank is almost empty), fuel is injected during 6.5 seconds. In a ...”
March 7, 2019
Brent@GMATPrepNow posted a reply to What is the sum of all of the integers in the chart above? in the Problem Solving forum
“Always check the answer choices BEFORE solving the question!! Since the answer choices are nicely spread apart, we can be quite aggressive in our estimation Let''s add the 5 numbers in each COLUMN COLUMN 1: Sum ≈500 COLUMN 2: Sum ≈-1000 COLUMN 3: Sum ≈1500 COLUMN 4: Sum ≈-2000 ...”
March 6, 2019
Brent@GMATPrepNow posted a reply to If 0.02 < x < 0.04 and 100 < y < 250, which of t in the Problem Solving forum
“We can use a nice (and often tested) fraction property that says: (a - b)/c = a/c - bc So, (y-x)/(xy) = y/xy - x/xy = 1/x - 1/y That''s better! So, we''re now looking for a possible value of 1/x - 1/y Let''s look at some EXTREME values. We can MAXIMIZE the value of 1/x - 1/y by MAXIMIZING ...”
March 6, 2019
Brent@GMATPrepNow posted a reply to For every even positive integer m, f(m) represents the in the Problem Solving forum
“f(24) = 2 x 4 x 6 x 8 x 10 x 12 x 14 x 16 x 18 x 20 x 22 x 24 Rewrite as prime factorization: f(24) = 2 x (2)(2) x (2)(3) x (2)(2)(2) x (2)(5) x (2)(2)(3) x (2)(7) x (2)(2)(2)(2) x (2)(3)(3) x (2)(2)(5) x (2)(11) x (2)(2)(2)(3) Answer: E ASIDE: As you can see from the answer choice, I ...”
March 6, 2019
fskilnik@GMATH posted a reply to The figure above shows the representations of the graphs of in the Problem Solving forum
“https://i.postimg.cc/QtpV8gKg/05-Mar19-5z.gif $$? = g\left( {f\left( 0 \right)} \right)$$ $$\leftGMATH method. Regards, Fabio.” March 5, 2019 Brent@GMATPrepNow posted a reply to Is xy>3? in the Data Sufficiency forum “Target question: Is xy > 3 ? Statement 1: (7^x) > 729 Since there''s no information about y, we cannot answer the target question with certainty. Statement 1 is NOT SUFFICIENT Statement 2: (9^y) = 7 Since there''s no information about x, we cannot answer the target question with ...” March 5, 2019 fskilnik@GMATH posted a reply to Karina´s mother has already bought T attraction tickets to in the Data Sufficiency forum “$$N\,\, = \,\,\,\# \,\,{\rm{friends}}? = 4N - T\left( 1 \right)\,\,T = 2N + 25\,\,\,\,\left\{ \matrix{ \,{\rm{Take}}\,\,\left( {N,T} \right) = \left( {20,65} \right)\,\,\,\,\, \Rightarrow \,\,\,\,{\rm{?}}\,\,{\rm{ = }}\,\,15 \hfill \cr \,{\rm{Take}}\,\,\left( {N,T} \right) = ...”
March 5, 2019
fskilnik@GMATH posted a reply to A triangle of area 30 is formed by the line x/c + y/(c+7) - in the Problem Solving forum
“Yes... 5-12-13 is an important GMAT Pythagorean Triple... $$?\,\, = \,\,\Delta \,\,{\rm{perimeter}}$$ $${S_\Delta } = 30\,\,\,\left( * \right)$$ $${x \over c} + {y \over {c + 7}} = 1\,\,\,\, \Rightarrow \,\,\,\,\left\{ \matrix{ \,x{\rm{ - intercept}} = c \hfill \cr \,y{\rm{ - ...” March 5, 2019 fskilnik@GMATH posted a reply to Is xy>3? in the Data Sufficiency forum “$$xy\,\,\mathop > \limits^? \,\,3\left( 1 \right)\,\,{7^x} > 729\,\,\,\left\{ \matrix{ \,{\rm{Take}}\,\,\left( {x,y} \right) = \left( {4,0} \right)\,\,\,\,\,\leftGMATH method. Regards, Fabio.”
March 5, 2019
fskilnik@GMATH posted a new topic called Is xy>3? in the Data Sufficiency forum
“GMATH practice exercise (Quant Class 14) Is xy > 3 ? (1) (7^x) > 729 (2) (9^y) = 7 Answer: _____(C)__ P.S.: this IS in GMAT´s quant section scope.”
March 5, 2019
fskilnik@GMATH posted a new topic called The figure above shows the representations of the graphs of in the Problem Solving forum
“GMATH practice exercise (Quant Class 13) https://i.postimg.cc/VNyhqzps/05-Mar19-4q.gif The figure above shows the representations of the graphs of the functions f and g, where f(x) = 2^(-0.5x) and g(x) = ax^2+b (a and b constants). What is the value of g(f(0)) ? (A) 3 (B) 3.25 (C) ...”
March 5, 2019
fskilnik@GMATH posted a new topic called Karina´s mother has already bought T attraction tickets to d in the Data Sufficiency forum
“GMATH practice exercise (Quant Class 14) Karina´s mother has already bought T attraction tickets to distribute to Karina´s friends for the party at the Alice-In-Wonderland amusement park. How many extra attraction tickets must Karina´s mother buy if Karina decides to give four tickets to each ...”
March 5, 2019
fskilnik@GMATH posted a new topic called A triangle of area 30 is formed by the line x/c + y/(c+7) - in the Problem Solving forum
“GMATH practice exercise (Quant Class 20) A triangle of area 30 is formed by the line x/c + y/(c+7) - 1 = 0 (where c is a positive constant) and the coordinate axes. What is the perimeter of this triangle? (A) 12 (B) 24 (C) 30 (D) 36 (E) 52 Answer: _____(C)__”
March 5, 2019
Brent@GMATPrepNow posted a reply to x is the product of all even numbers from 2 to 50, inclusive in the Problem Solving forum
“Here''s a very similar (official) question to practice with: https://www.beatthegmat.com/arthemetic-question-on-factors-and-prime-numbers-t275643.html Cheers, Brent”
March 5, 2019
Brent@GMATPrepNow posted a reply to Joey works at a clothing store and receives an employee in the Problem Solving forum
“Let R = REGULAR price of the item Joey and receives an employee discount of 10 percent off the regular price of any item. So, Joey pays 90% of the REGULAR price. In other words, 0.9R = the DISCOUNT price that Joey actually pays What is the regular price of an item that Joey purchases for ...”
March 5, 2019
Brent@GMATPrepNow posted a reply to In how many ways can 16 different gits be divided among four in the Problem Solving forum
“Let''s say the children are named A, B, C, and D Stage 1: Select 4 gifts to give to child A Since the order in which we select the 4 gifts does not matter, we can use combinations. We can select 4 gifts from 16 gifts in 16C4 ways (= 16!/(4!)(12!)) So, we can complete stage 1 in ...”
March 4, 2019
fskilnik@GMATH posted a reply to Ian Stewart GMAT quant books in the GMAT Math forum
“Dear aflaam messih, Thank you for your kind words. We are happy to use our GMAT experience to contribute to this wonderful community. Feedbacks like yours are marvelous. They tell us we are in the right direction! See you in other posts and success in your studies! Fabio.”
March 4, 2019
fskilnik@GMATH posted a reply to If (2x+y-z)^2 + (x-y)^2 + (z-3)^2 = -(3y-z)^2 , what is the in the Problem Solving forum
“$$? = 3x + 2y + z$$ $${\left( {2x + y - z} \right)^2} + {\left( {x - y} \right)^2} + {\left( {z - 3} \right)^2} = - {\left( {3y - z} \right)^2}\,\,\,\,\,\left( * \right)$$ $$\left. \matrix{ {\left( {2x + y - z} \right)^2} + {\left( {x - y} \right)^2} + {\left( {z - 3} \right)^2}\,\,\, \ge ...” March 4, 2019 fskilnik@GMATH posted a reply to If a<b<0 are integers, what is the value of a^3-b^3? in the Data Sufficiency forum “$$? = {a^3} - {b^3}\,a < b < 0\,\,\,{\rm{ints}}\,\,\,\,\left( * \right)\left( 1 \right)\,\,\,\left\{ \matrix{ \,\left( {a + b} \right)\left( {a - b} \right) = 65 = 1 \cdot 65 = 5 \cdot 13 \hfill \cr \,\left( * \right)\,\,\,\,\, \Rightarrow \,\,\,\,\,a + b < a - b\,\,\, ...”
March 4, 2019
fskilnik@GMATH posted a new topic called If a<b<0 are integers, what is the value of a^3-b^3? in the Data Sufficiency forum
“GMATH practice exercise (Quant Class 16) https://i.postimg.cc/rF138gcp/03-Mar19-13q.gif Answer: ____(C)__”
March 4, 2019
fskilnik@GMATH posted a reply to What is the value of (2-1/3)(1+1/4)^(-1)(1+2/5)? in the Problem Solving forum
“$$\,? = \left( {2 - {1 \over 3}} \right){\left( {1 + {1 \over 4}} \right)^{ - 1}}\left( {1 + {2 \over 5}} \right)\,\,$$ $$\left. \matrix{ 2 - {1 \over 3} = {{2 \cdot 3} \over 3} - {1 \over 3} = {5 \over 3} \hfill \cr 1 + {1 \over 4} = {5 \over 4}\,\,\,\,\, \Rightarrow \,\,\,\,\,{\left( {1 + ...” March 3, 2019 fskilnik@GMATH posted a reply to If (a,b)=(9,8), the expression 2(a^3-b^3)/(a(a+b)+b^2) is: in the Problem Solving forum “$$?\,\, = \,\,{{2\left( {{a^3} - {b^3}} \right)} \over {a\left( {a + b} \right) + {b^2}}}\,\,\,\,\,{\rm{for}}\,\,\,\,\left( {a,b} \right) = \left( {9,8} \right)\left. \matrix{ 2\left( {{a^3} - {b^3}} \right) = 2\left( {a - b} \right)\left( {{a^2} + ab + {b^2}} \right)\,\,\, \hfill \cr ...”
March 3, 2019
fskilnik@GMATH posted a reply to When defined, the expression (x^2-y^2)/(xy)-(xy-y^2)/(xy-x^2 in the Problem Solving forum
“$$? = \frac{{{x^2} - {y^2}}}{{xy}} - \frac{{xy - {y^2}}}{{xy - {x^2}}}\,\,\,$$ $$\frac{{xy - {y^2}}}{{xy - {x^2}}} = \frac{{y\left( {x - y} \right)}}{{x\left( {y - x} \right)}} = \underleftrightarrow {\frac{{ - y\left( {y - x} \right)}}{{x\left( {y - x} \right)}}} = \frac{{ - y}}{x}$$ $$? = ...” March 3, 2019 fskilnik@GMATH posted a new topic called If (a,b)=(9,8), the expression 2(a^3-b^3)/(a(a+b)+b^2) is: in the Problem Solving forum “GMATH practice exercise (Quant Class 3) https://i.postimg.cc/9QDKH2xG/03-Mar19-12s.gif Answer: _____(C)__” March 3, 2019 fskilnik@GMATH posted a reply to If line AC bisects angle BCD, what is the measure of angle A in the Problem Solving forum “https://i.postimg.cc/L6zxMXRK/03-Mar19-9h.gif$$? = x\Delta BCE\,\,:\,\,\,20 + x = 180 - \left( {110 + 20} \right)\,\,\,\,\, \Rightarrow \,\,\,\,\,? = x = 30$$The correct answer is (B). We follow the notations and rationale taught in the GMATH method. Regards, Fabio.” March 3, 2019 fskilnik@GMATH posted a new topic called If (2x+y-z)^2 + (x-y)^2 + (z-3)^2 = -(3y-z)^2 , what is the in the Problem Solving forum “GMATH practice exercise (Quant Class 3) https://i.postimg.cc/cJWTHNxg/03-Mar19-11p.gif Answer: ______(A)__” March 3, 2019 fskilnik@GMATH posted a new topic called When defined, the expression (x^2-y^2)/(xy)-(xy-y^2)/(xy-x^2 in the Problem Solving forum “GMATH practice exercise (Quant Class 3) https://i.postimg.cc/sgHDf39K/03-Mar19-8f.gif Answer: _____(A)__” March 3, 2019 fskilnik@GMATH posted a new topic called If line AC bisects angle BCD, what is the measure of angle A in the Problem Solving forum “GMATH practice exercise (Quant Class 1) If line AC bisects angle BCD, what is the measure of angle ADC? https://i.postimg.cc/m2qQcWwZ/03-Mar19-6y.gif (A) 20 degrees (B) 30 degrees (C) 40 degrees (D) 45 degrees (E) 50 degrees Answer: ____(B)__” March 3, 2019 fskilnik@GMATH posted a new topic called What is the value of (2-1/3)(1+1/4)^(-1)(1+2/5)? in the Problem Solving forum “GMATH practice exercise (Quant Class 1) https://i.postimg.cc/br4jnvr9/03-Mar19-3q.gif Answer: _____(D)__” March 3, 2019 Brent@GMATPrepNow posted a reply to The positive two-digit integers x and y have the same digits in the Problem Solving forum “Another approach is to test some values for x and y that satisfy the given information. Positive two-digit integers x and y have the same digits, but in reverse order So, it COULD be the case that x = 12 and y = 21 Which of the following must be a factor of x + y? x + y = 12 + 21 = 33 ...” March 3, 2019 Brent@GMATPrepNow posted a reply to Median of set T in the Problem Solving forum “If we have a set of y INTEGERS, there are two possible cases when it comes to the MEDIAN. Case a: y is an ODD number, in which case the MEDIAN equals the one middle integer (when all of the integers are arranged in ascending order). In this case, the median must be an integer. Case b: y is an ...” March 2, 2019 fskilnik@GMATH posted a reply to From the figure shown, each of N people was asked to take 7 in the Problem Solving forum “https://i.postimg.cc/1XW4BFjw/01-Mar19-9b.gif$$?\,\, = \,\,\left( {\# \,\,{\rm{possible}}\,\,\Delta \,\,{\rm{equilateral}}\,\,{\rm{configurations}}} \right)\,\,{\rm{ + }}\,\,{\rm{1}}? = 15 + 1 = 16$$The correct answer is (D). We follow the notations and rationale taught in the ...” March 1, 2019 fskilnik@GMATH posted a reply to Oneyde and Jorge must make two reservations for a trip, in w in the Problem Solving forum “$$?\,\,\,\,:\,\,\,\# \,\,\,O,J\,\,{\rm{positions}}\,\,{\rm{with}}\,\,{\rm{restrictions}}{\rm{4 - seats}}\,\,{\rm{group}}\,\,{\rm{(left)}}\,\,{\rm{:}}\,\,{\rm{6}}\,\,{\rm{possibilities}}\,\,\,\left\{ \matrix{ \,\left( {O,J,e,e} \right)\,\,{\rm{or}}\,\,\left( {J,O,e,e} \right) \hfill \cr ...”
March 1, 2019
fskilnik@GMATH posted a new topic called Oneyde and Jorge must make two reservations for a trip, in w in the Problem Solving forum
“GMATH practice exercise (Quant Class 18) https://i.postimg.cc/W31dkS9T/01-Mar19-12a.gif Oneyde and Jorge must make two reservations for a trip, in which only 9 seats are still available, all of them in row F (see figure). If they want to sit next to each other, without being separated by ...”
March 1, 2019
fskilnik@GMATH posted a new topic called From the figure shown, each of N people was asked to take 7 in the Problem Solving forum
“GMATH practice exercise (Quant Class 18) https://i.postimg.cc/prJBksfr/01-Mar194z.gif From the figure shown, each of N people will be asked to take 7 points out, so that the 3 points left form vertices of an equilateral triangle. If all of them proceed correctly, what is the minimum value of ...”
March 1, 2019
fskilnik@GMATH posted a reply to What is the value of k? in the Data Sufficiency forum
“https://i.postimg.cc/JhzCQJM1/01-Mar19-4q.gif $$? = k\,\,\,\leftGMATH method. Regards, Fabio.” March 1, 2019 fskilnik@GMATH posted a reply to If (2^a)*3^(b-1) = (18^b)/2, what is the value of ab? in the Problem Solving forum “$$? = \,\,ab{2^a} \cdot {3^{b - 1}} = {{{{18}^b}} \over 2}\,\,\,\,\,\mathop \Rightarrow \limits^{ \cdot \,2} \,\,\,\,\,{2^{a + 1}} \cdot {3^{b - 1}}\, = {\left( {2 \cdot {3^2}} \right)^b} = {2^b} \cdot {3^{2b}}{2^{a + 1 - b}} = {3^{2b - \left( {b - 1} \right)}}\,\,\,\,\,\mathop ...”
February 28, 2019
fskilnik@GMATH posted a reply to Planifying the lateral surface area of a cone, we get the ci in the Problem Solving forum
“https://i.postimg.cc/0Qyn3DSH/28-Feb19-4y.gif $$?\,\, \cong \,\,h$$ $${\text{circular}}\,\,{\text{base}}\,{\text{of}}\,\,{\text{cone}}\,\,:\,\,\,\,2\pi r\,\, = \,\,\frac{{{{160}^ \circ }}}{{{{360}^ \circ }}}\left( {2\pi \cdot 18} \right)\,\,\,\,\, \Rightarrow \,\,\,\,\,r = \frac{{16 \cdot ...” February 28, 2019 Brent@GMATPrepNow posted a reply to Two positive numbers differ by 12 and their reciprocals in the Problem Solving forum “Two positive numbers differ by 12 Let x = the smaller number So x + 12 = the larger number NOTE: our goal is to find the value of x(x + 12) Their reciprocals differ by 4/5 We get: 1/x - 1/(x+12) = 4/5 Multiply both sides by x to get: 1 - x/(x + 12) = 4x/5 Multiply both sides by 5 to get: 5 ...” February 28, 2019 Brent@GMATPrepNow posted a reply to In a town of 8,000 residents, 65 percent of all residents in the Problem Solving forum “Another approach is to use the Double Matrix Method. This technique can be used for most questions featuring a population in which each member has two characteristics associated with it (aka overlapping sets questions). Here, we have a population of residents, and the two characteristics are: ...” February 28, 2019 fskilnik@GMATH posted a new topic called What is the value of k? in the Data Sufficiency forum “GMATH practice exercise (Quant Class 15) https://i.postimg.cc/QNk4tN8b/28-Feb19-9j.gif What is the value of k? (1) x = 2 (2) y^2 = 3 Answer: ____(C)___” February 28, 2019 fskilnik@GMATH posted a new topic called If (2^a)*3^(b-1) = (18^b)/2, what is the value of ab? in the Problem Solving forum “GMATH practice exercise (Quant Class 3) https://i.postimg.cc/SsG5YcFy/28-Feb19-6t.gif Answer: ____(E)__” February 28, 2019 fskilnik@GMATH posted a new topic called Planifying the lateral surface area of a cone, we get the ci in the Problem Solving forum “GMATH practice exercise (Quant Class 11) https://i.postimg.cc/zBvv4GGk/28-Feb19-3w.gif Planifying the lateral surface area of a cone, we get the circular sector with center O and radius 18 shown in the figure. Which of the following is closest to the length of the height of this cone? (A) ...” February 28, 2019 fskilnik@GMATH posted a reply to If the line segment AB is one of the sides of a regular poly in the Data Sufficiency forum “https://i.postimg.cc/zvXz514z/27-Feb19-9k.gif$${\rm{regular}}\,\,N{\rm{ - polygon}}\,\,\left( {N \ge 3\,\,{\mathop{\rm int}} } \right)? = N\left( 1 \right)\,\,\alpha = {30^ \circ }\,\,\,\, \Rightarrow \,\,\,\angle AOB = {60^ \circ }\,\,\,\left( {{\rm{central}}\,\,{\rm{angle}}} ...”
February 28, 2019
fskilnik@GMATH posted a reply to What is the value of DE/FG ? in the Data Sufficiency forum
“$$\Delta ADE\,\,\, \cong \,\,\,\Delta AFG\,\,\, \cong \,\,\,\Delta ABC$$ $$? = \frac{{DE}}{{FG}}\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\boxed{\,\,?\,\, = \,\,\,\Delta ADE:\Delta AFG\,\,\,{\text{ratio}}\,\,{\text{of}}\,\,{\text{similarity}}\,\,{\text{ = }}\,\,\,\frac{{AD}}{{AF}}\,\,\left( { = ...” February 28, 2019 Brent@GMATPrepNow posted a reply to Working simultaneously and independently at an identical con in the Problem Solving forum “Let''s assign a nice value to x (a value that will work well with all of the numbers 3, 4 and 6. Let''s say x = 24 GIVEN: 4 machines make x units in 6 days This means 4 machines make 24 units in 6 days So, 4 machines make 4 units in 1 day So, 1 machine makes 1 unit in 1 day From here, ...” February 28, 2019 Brent@GMATPrepNow posted a reply to A certain club has 20 members. What is the ratio of the in the Problem Solving forum “5-member committees Since the order in which we select the committee members does not matter, we can use COMBINATIONS We can select 5 people from 20 people in 20C5 ways 20C5 = (20)(19)(18)(17)(16)/(5)(4)(3)(2)(1) 4-member committees Since the order in which we select the committee members ...” February 28, 2019 Brent@GMATPrepNow posted a reply to Train A and Train B began traveling towards each other from in the Problem Solving forum “This is a SHRINKING GAP question. Train A traveled at 35 miles per hour and Train B traveled at 25 miles per hour, 35 mph + 25 mph = 60 mph So, the gap CLOSES at a rate of 60 mph Train A and Train B began traveling towards each other from opposite ends of a 500-mile long track at 1:00 PM ...” February 28, 2019 fskilnik@GMATH posted a reply to A large rectangular decorative panel of 45 meters (horizonta in the Problem Solving forum “$${\rm{panel}}\,\,:\,\,\,4500\,{\rm{cm}}\,\, \times \,\,\,600\,{\rm{cm}}M\,\,{\rm{squares}}\,\,{\rm{:}}\,\,\,k\,{\rm{cm}}\,\, \times \,\,\,k\,{\rm{cm}}\,\,\,{\rm{each}}\,\,\,\,\,\,\,\left( {k \ge 1\,\,{\mathop{\rm int}} } \right){\rm{?}}\,\, = \,\,\,\min \left( M \right)\left. ...”
February 28, 2019
fskilnik@GMATH posted a new topic called If the line segment AB is one of the sides of a regular poly in the Data Sufficiency forum
“GMATH practice exercise (Quant Class 15) https://i.postimg.cc/13f7VYDv/27-Feb19-4q.gif Answer: ____(A)__”
February 28, 2019
Brent@GMATPrepNow posted a reply to In 1990 the budgets for projects Q and V were $660,000 and in the Problem Solving forum “One approach is to treat this is a rate question. In 1990 the GAP BETWEEN V''s budget and Q''s budget was$120,000 ($780,000 -$660,000 = $120,000) Each year, the budget for Q increased by$30,000 and the budget for V decreased by $10,000. In other words, the GAP BETWEEN the budgets ...” February 28, 2019 fskilnik@GMATH posted a reply to Ian Stewart GMAT quant books in the GMAT Math forum “Hi! I have made Ian know about your interest in his materials a minute ago. I believe he will be here soon to contact you. Regards and have great studies with his (I am certain) outstanding collection, Fabio.” February 27, 2019 fskilnik@GMATH posted a new topic called What is the value of DE/FG ? in the Data Sufficiency forum “GMATH practice exercise (Quant Class 17) https://i.ibb.co/tDdzQZJ/27-Feb19-3j.gif What is the value of DE/FG ? (1) AB/AD = 5 (2) AD = FB Answer: ____(C)__” February 27, 2019 fskilnik@GMATH posted a new topic called A large rectangular decorative panel of 45 meters (horizonta in the Problem Solving forum “GMATH practice exercise (Quant Class 16) A large rectangular decorative panel of 45 meters (horizontal dimension) by 6 meters (vertical dimension) is to be completely divided into M identical squares, all of them with horizontal and vertical edges. If the smallest measure of length considered for ...” February 27, 2019 fskilnik@GMATH posted a reply to During a 3h-experiment, the number of bacteria increased fro in the Problem Solving forum “$$f\left( t \right) = a \cdot {b^t}\,\,\,{\rm{bacteria}}\,\,\,\,\,\left( {{\rm{at}}\,\,t \ge 0\,\,{\rm{hours}}} \right)$$ $$? = f\left( {{1 \over 2}} \right) = a \cdot \sqrt b$$ $$\left( {0\,;\,{{10}^4}} \right) \in \,\,{\rm{graph}}\left( f \right)\,\,\,\, \Rightarrow \,\,\,\,{10^4} = a \cdot ...” February 27, 2019 fskilnik@GMATH posted a reply to In the rectangular coordinate system, what is the area of th in the Problem Solving forum “https://i.ibb.co/drKdnk4/26-Feb19-5z.gif$$? = {S_{{\rm{shaded}}}}\,\,\,:\,\,\,\,\left\{ \matrix{ \,xy > 0\, \hfill \cr \,0 < y < 2\,\,\,\, \hfill \cr \,x < y + 1 \hfill \cr} \right.\,\,\,\,\,\, \cong \,\,\,\,\,\,\,\,\,\left\{ \matrix{ \,x > 0\, \hfill \cr \,0 ...” February 27, 2019 fskilnik@GMATH posted a reply to In the rectangular coordinate system, what is the area of th in the Problem Solving forum “The "image of the system" is part of the solution! As you will see below, it is almost the whole solution itself! Regards, Fabio.” February 27, 2019 fskilnik@GMATH posted a reply to If x, y, and z are integers such that 67500 is divisible by in the Problem Solving forum “$$? = \max \left( {3x + 2y + z} \right)\,\,\,\left( * \right)$$ $$x,y,z\,\,\mathop \ge \limits^{\left( * \right)} \,\,0\,\,\,{\rm{ints}}\,\,\,\left( {**} \right)$$ $$67500 = \underleftrightarrow {675 \cdot 100} = 25 \cdot 27 \cdot 4 \cdot 25 = {2^2} \cdot {3^3} \cdot {5^4}$$ $$54 = 2 \cdot 27 ...” February 27, 2019 fskilnik@GMATH posted a reply to In the equality above, A,B,C are positive integers. What is in the Problem Solving forum “$$A,B,C\,\, \ge 1\,\,\,{\rm{ints}}\,\,\,\left( * \right){{71} \over {11}} = A + {1 \over {B + {{\left( {C + 1} \right)}^{ - 1}}}}? = 2A + 3B - 4C\left. \matrix{ B + {1 \over {C + 1}}\,\,\mathop > \limits^{\left( * \right)} \,\,1\,\,\,\,\, \Rightarrow \,\,\,\,\,0 < \,{1 ...” February 27, 2019 fskilnik@GMATH posted a reply to What is the value of a+b? in the Data Sufficiency forum “$$? = a + b$$ $$\left( 1 \right)\,\,a\left( {a + b - 2} \right) = 91\,\,\,\,:\,:\,\,\,\left\{ \matrix{ \,{\rm{Take}}\,\,\left( {a,b} \right) = \left( {91,\, - 88} \right)\,\,\,\, \Rightarrow \,\,\,? = 3\,\, \hfill \cr \,{\rm{Take}}\,\,\left( {a,b} \right) = \left( {1,92} \right)\,\,\,\, ...” February 27, 2019 fskilnik@GMATH posted a new topic called In the rectangular coordinate system, what is the area of th in the Problem Solving forum “GMATH practice exercise (Quant Class 20) https://i.ibb.co/NLBX1Wj/26-Feb19-7d.gif Answer: ____(C)__” February 26, 2019 fskilnik@GMATH posted a new topic called During a 3h-experiment, the number of bacteria increased fro in the Problem Solving forum “GMATH practice exercise (Quant Class 12) https://i.ibb.co/QDJ1ShL/26-Feb19-4q.gif During a 3h-experiment, the number of bacteria increased from 10^4 (at the start) to 8 times this value (at the end), according to a biological law associated with an exponential function (as shown), where a and ...” February 26, 2019 fskilnik@GMATH posted a new topic called If x, y, and z are integers such that 67500 is divisible by in the Problem Solving forum “GMATH practice exercise (Quant Class 16) If x, y, and z are integers such that 67500 is divisible by (2^x)(3^y)(5^z) and (2^x)(3^y)(5^z) is NOT a multiple of 54, what is the maximum possible value of 3x+2y+z? (A) 15 (B) 14 (C) 13 (D) 12 (E) less than 12 Answer: _____(B)__” February 26, 2019 fskilnik@GMATH posted a new topic called In the equality above, A,B,C are positive integers. What is in the Problem Solving forum “GMATH practice exercise (Quant Class 1) https://i.ibb.co/C7pD425/26-Feb19-3w.gif Answer: ____(C)__” February 26, 2019 fskilnik@GMATH posted a new topic called What is the value of a+b? in the Data Sufficiency forum “GMATH practice exercise (Quant Class 14) What is the value of a+b ? (1) a^2+ab−2a=91 (2) b^2+ab−2b=−28 Answer: ____(E)__” February 26, 2019 Brent@GMATPrepNow posted a reply to Is xy+zt+yz+tx positive? in the Data Sufficiency forum “Target question: Is xy + zt + yz + tx positive? Statement 1: |x| = |y| = |z| = t Let''s TEST some values. There are several values of x, y, z and t that satisfy statement 1. Here are two: Case a: x = y = z = t = 1. In this case, xy + zt + yz + tx = (1)(1) + (1)(1) + (1)(1) + (1)(1) = 4. ...” February 26, 2019 Brent@GMATPrepNow posted a reply to A manufacturer makes umbrellas at the cost of c dollars per in the Problem Solving forum “This is a tough one to use the INPUT-OUTPUT approach, but here is goes: Let c = 2 (it cost 2 to make each umbrella) Let x = 10 (we make 10 umbrellas) Let r = 5 (the retail price is 5 per umbrella) Let b = 0 (the below-cost sale price is 0 per umbrella) So, the manufacturer made 10 ...” February 26, 2019 fskilnik@GMATH posted a reply to What is the difference between the areas of the squares ABCD in the Data Sufficiency forum “$$?\,\, = \,\,{S_{{\rm{ABCD}}}} - {S_{{\rm{EFGC}}}}$$(Click on the image to have it "zoomed"!) https://i.ibb.co/KhpKxCh/25-Feb19-6r.gif$$\left. \matrix{ \left( {1 + 2} \right)\,\,\,\,? = \,{\left( {5k} \right)^2} - {\left( {3k} \right)^2} = 16{k^2} \hfill \cr 30 = ...” February 26, 2019 fskilnik@GMATH posted a reply to Is xy+zt+yz+tx positive? in the Data Sufficiency forum “$$\underline {xy} + \underline{\underline {zt}} + \underline {yz} + \underline{\underline {tx}} \,\,\mathop > \limits^? \,\,0\,\,\,\,\, \Leftrightarrow \,\,\,\,\,y\left( {x + z} \right) + t\left( {z + x} \right) = \left( {x + z} \right)\left( {y + t} \right)\,\,\,\mathop > \limits^? ...” February 26, 2019 fskilnik@GMATH posted a reply to If x^3 (x^2+y^2) = z^2 , is xyz = 0 ? in the Data Sufficiency forum “$${x^3}\left( {{x^2} + {y^2}} \right) = {z^2}\,\,\,\,\,\left( * \right)xyz \,\, \mathop = \limits^? \,\,0\left( {1 + 2} \right)\,\,\left\{ \matrix{ \,{y^3}\left( {{y^2} + {z^2}} \right) = {x^2}\,\,\left( * \right) \hfill \cr \,{z^3}\left( {{z^2} + {x^2}} \right) = ...” February 26, 2019 fskilnik@GMATH posted a new topic called If x^3(x^2+y^2) = z^2 , is xyz = 0 ? in the Data Sufficiency forum “GMATH practice exercise (Quant Class 14) If x^3 (x^2+y^2) = z^2 , is xyz = 0 ? (1) y^3 (y^2+z^2) = x^2 (2) z^3 (z^2+x^2) = y^2 Answer: ____(E)__” February 25, 2019 fskilnik@GMATH posted a new topic called Is xy+zt+yz+tx positive? in the Data Sufficiency forum “GMATH practice exercise (Quant Class 14) Is xy+zt+yz+tx positive? (1) |x| = |y| = |z| = t (2) x+y+z+t = 0 Answer: ____(B)__” February 25, 2019 fskilnik@GMATH posted a new topic called What is the difference between the areas of the squares ABCD in the Data Sufficiency forum “GMATH practice exercise (Quant Class 15) https://i.ibb.co/9mxGjhk/25-Feb19-4q.gif What is the difference between the areas of the squares ABCD and EFGC, in that order? (1) The area of the shaded triangle CDE is 30. (2) The ratio of the areas of the squares ABCD and EFGC, in that order, ...” February 25, 2019 fskilnik@GMATH posted a reply to Nine identical chips are numbered from 1 to 9 (one different in the Problem Solving forum “ $$?\,\,\mathop = \limits^{\left( * \right)} \,\,\,\# \,\,\left( {{\text{odd,even,odd,even,odd,even,odd,even,odd}}} \right)\,\,{\text{tuples}}$$ $$\left( * \right)\,\,{\text{must}}\,\,{\text{start}}\,\,{\text{and}}\,\,{\text{finish}}\,\,{\text{with}}\,\,{\text{odd numbers}}\,\,\,\left( ...” February 25, 2019 fskilnik@GMATH posted a reply to How many positive two-digit numbers are odd, not divisible b in the Problem Solving forum “$$?\,\,\,\,:\,\,\,\# N\,,\,\,N \in \leftGMATH method. Regards, Fabio.” February 25, 2019 fskilnik@GMATH posted a reply to You have access to an unlimited number of each of the follow in the Problem Solving forum “$$?\,\,\,:\,\,\,{\rm{possible}}\,\,{\rm{amounts}}\,\,\,\,\left( {{\rm{with}}\,\,6\,\,{\rm{coins}}} \right)$$ $${\rm{I}}.\,\,\,76 = 1 \cdot 1 + 3 \cdot 25 = 1 \cdot 1 + 2 \cdot 25 + 2 \cdot 10 + 1 \cdot 5\,\,\,\, \Rightarrow ...” February 25, 2019 fskilnik@GMATH posted a reply to If G is a function defined in the positive integers, such th in the Data Sufficiency forum “$$? = G\left( {G\left( {2019} \right)} \right)\left( 1 \right)\,\,\,\left\{ \matrix{ \,G\left( {G\left( {m + n} \right)} \right) = m + n\,\,\,\left( {m,n \ge 1\,\,{\rm{ints}}} \right) \hfill \cr \,\,\,\,\,\,{\rm{Take}}\,\,\left( {m,n} \right) = \left( {2018,1} \right) \hfill \cr} ...” February 25, 2019 fskilnik@GMATH posted a reply to For each positive integer n, the nth positive triangular num in the Problem Solving forum “$${T_n} = 1 + 2 + \ldots + n\,\,\mathop = \limits^{\left( * \right)} \,\,{{n \cdot \left( {n + 1} \right)} \over 2}\,\,\,\,\,\,\,\left( {n \ge 1\,\,{\mathop{\rm int}} } \right)\,\,\,\,\,\,\,\,\,\,\,\leftGMATH method. Regards, Fabio.” February 25, 2019 Brent@GMATPrepNow posted a reply to How many positive two-digit numbers are odd, not divisible b in the Problem Solving forum “After about 30 seconds, I recognized that I couldn''t see a nice straightforward solution (one that doesn''t involve considering multiple cases), so I had 3 options: 1) Keep searching for a nice straightforward solution 2) Guess and move on 3) List the possible outcomes Since the answer ...” February 25, 2019 Brent@GMATPrepNow posted a reply to Nine identical chips are numbered from 1 to 9 (one different in the Problem Solving forum “ODDS: 1, 3, 5, 7, 9 EVENS: 2, 4, 6, 8 Take the task of removing the 9 chips and break it into stages. Stage 1: Select an ODD number to be the 1st selection There are 5 ODDs to choose from. So, we can complete stage 1 in 5 ways Stage 2: Select an EVEN number to be the 2nd selection ...” February 25, 2019 fskilnik@GMATH posted a new topic called Nine identical chips are numbered from 1 to 9 (one different in the Problem Solving forum “GMATH practice exercise (Quant Class 18) Nine identical chips are numbered from 1 to 9 (one different number per chip) and placed in a box. There are N ways in which all the chips are taken out from the box, one at a time and without repositions, in a sequence of alternating odd and even numbers. ...” February 25, 2019 fskilnik@GMATH posted a new topic called How many positive two-digit numbers are odd, not divisible b in the Problem Solving forum “GMATH practice exercise (Quant Class 16) How many positive two-digit numbers are odd, not divisible by 3, and have distinct digits? (A) 28 (B) 27 (C) 26 (D) 25 (E) 24 Answer: ____(B)__” February 25, 2019 Brent@GMATPrepNow posted a reply to All assets in Karina's investment portfolio are divided betw in the Problem Solving forum “Let''s say Karina''s entire portfolio is worth 100 altogether. So, we want to divide this 100 into four integer amounts: w, x, y, z, where w < x < y < z, and we want to minimize the value of z In order to MINIMIZE the value of the z, we must MAXIMIZE the values of w, x, and y. Now ...” February 25, 2019 Brent@GMATPrepNow posted a reply to Vivian drives to her sister’s house and back. She takes th in the Problem Solving forum “One approach is to assign a "nice" value (one that works well with 50 mph and 70 mph) to the distance her sister''s house. So, let''s say the distance is 350 miles Average speed = (total distance traveled)/(total travel time) TOTAL distance = 350 miles + 350 miles = 700 miles ...” February 25, 2019 fskilnik@GMATH posted a new topic called You have access to an unlimited number of each of the follow in the Problem Solving forum “GMATH practice exercise (Quant Class 3) You have access to an unlimited number of each of the following coins: pennies, nickels, dimes and quarters. Which of the following amounts CAN be made using exactly 6 of these coins? I. 76 cents II. 81 cents III. 29 cents IV. 101 cents (A) None of ...” February 24, 2019 fskilnik@GMATH posted a new topic called If G is a function defined in the positive integers, such th in the Data Sufficiency forum “GMATH practice exercise (Quant Class 14) If G is a function defined in the positive integers, such that G(k) is a positive integer for each positive integer k, what is the value of G(G(2019)) ? (1) G(G(m+n))=m+n , for every positive integers m,n. (2) G(n)=m implies G(m)=n, for every positive ...” February 24, 2019 fskilnik@GMATH posted a new topic called For each positive integer n, the nth positive triangular num in the Problem Solving forum “GMATH practice exercise (Quant Class 17) https://i.ibb.co/qjVrNkW/24-Feb19-4z.gif For each positive integer n, the nth positive triangular number is equal to the number of dots in the triangular arrangement with n dots on a side. The first positive triangular numbers are 1, 3, 6, 10, 15, and ...” February 24, 2019 Brent@GMATPrepNow posted a reply to In a certain class, the ratio of girls to boys is 5:4. How m in the Data Sufficiency forum “ Given: In a certain class, the ratio of girls to boys is 5:4. Let G = number of girls in the class Let B = number of boys in the class We can write: G/B = 5/4 Cross multiply to get: 4G = 5B Rearrange to get: 4G - 5B = 0 Target question: What is the value of G Statement 1: If four ...” February 24, 2019 Brent@GMATPrepNow posted a reply to Kim has 40 percent more money than Sal and Sal has 20 in the Problem Solving forum “Let x = Phil''s money Sal has 20 percent LESS money than Phil So, Sal''s money = (Phil''s money) - (20% Phil''s money) = x - (20% of x) = x - 0.2x = 0.8x Kim has 40 percent more money than Sal So, Kim''s money = (Sal''s money) + (40% Sal''s money) = (0.8x) + (40% of 0.8x) = ...” February 24, 2019 Brent@GMATPrepNow posted a reply to A straight line in the xy-plane has a slope of 2 and a in the Problem Solving forum “The question conveniently gives us the information to write the equation of the line in slope y-intercept form, y = mx + b, where m = slope and b = the y-intercept. Line in the xy-plane has a slope of 2 and a y-intercept of 2 So, the equation of the line is: y = 2x + 2 On this line, what is ...” February 24, 2019 Brent@GMATPrepNow posted a reply to If y >= 0, What is the value of x? in the Data Sufficiency forum “Target question: What is the value of x? Given: y ≥ 0 Statement 1: |x - 3| ≥ y Let''s TEST some values. There are several values of x and y that satisfy statement 1. Here are two: Case a: x = 10 and y = 2. We get |10 - 3| ≥ 2, which evaluates to be 7 ≥ 2, which satisfies ...” February 23, 2019 Brent@GMATPrepNow posted a reply to The total of company C's assets in 1994 was 300% greater in the Problem Solving forum “The total of company C''s assets in 1992 was N dollars Company C''s assets in 1993 was 400% greater than the total in 1992 So, 1993 assets = (1992 assets) + (400% of 1992 assets) = (N) + (400% of N) = (N) + (400/100 x N) = N + 4N = 5N Company C''s assets in 1994 was 300% greater than the ...” February 23, 2019 Brent@GMATPrepNow posted a reply to At a bakery, the price of a bagel ranges between 0.65 and in the Problem Solving forum “The least expensive price for a bagel is 0.65 If a customer purchases 12 bagels (at 0.65 each), then he/she receives 13 bagels. So, the minimum amount that a customer could pay to receive 13 bagels = 12 x 0.65 = 7.80 Answer: B Cheers, Brent” February 23, 2019 fskilnik@GMATH posted a reply to In the figure shown, AB = AC = 12. Which of the following is in the Problem Solving forum “https://i.ibb.co/HHMzBxX/21-Feb19-4wq.gif$$?\,\, \cong \,\,\pi {r^2}$$Point O is equidistant from the rays AM and AN, hence AO must be contained in the angle bisector of angle MAN = angle BAC.$$\left\{ \matrix{ \,OM = r\,\,\,\left( {{{30}^ \circ }} \right) \hfill \cr \Delta ...” February 22, 2019 Brent@GMATPrepNow posted a reply to a, b, and c are positive integers. Is a+b+c an odd number? in the Data Sufficiency forum “ Given: a, b, and c are positive integers. Target question: Is a + b + c an odd number? Statement 1: ab is an odd number No information about c. NOT SUFFICIENT Statement 2: c is an odd number No information about a or b. NOT SUFFICIENT Statements 1 and 2 combined If ab ...” February 22, 2019 Brent@GMATPrepNow posted a reply to In how many ways a cricket team consisting of 5 batsmen, 4 in the Problem Solving forum “Take the task of creating a cricket team and break it into stages. Stage 1: Select 5 batsmen Since the order in which we select the batsmen does not matter, we can use combinations. We can select 5 batsmen from 7 batsmen in 7C5 ways (21 ways) So, we can complete stage 1 in 21 ways ...” February 22, 2019 Brent@GMATPrepNow posted a reply to If 1/x-1/y=1/z, what is the value of y, in terms of x and z? in the Problem Solving forum “We can also solve the question algebraically. GIVEN: 1/x - 1/y = 1/z Multiply both sides by x to get: 1 - x/y = x/z Multiply both sides by y to get: y - x = xy/z Multiply both sides by z to get: yz - xz = yx Rearrange to get y terms on one side: yz - yx = xz Factor left side: y(z - x) = ...” February 22, 2019 fskilnik@GMATH posted a reply to The graphs of the functions f and g are represented in In th in the Problem Solving forum “https://i.ibb.co/rmtCdPt/21-Feb19-4v.gif $$? = g\left( {g\left( { - 1} \right) + 1} \right) + f\left( {g\left( 3 \right) + 1} \right) = g\left( {A + 1} \right) + f\left( {B + 1} \right)$$ $$A\,\, = \,\,g\left( { - 1} \right) = 4\,\,\,\leftGMATH method. Regards, Fabio.” February 22, 2019 fskilnik@GMATH posted a reply to Brenda will test-drive a vintage motor car on a circular tra in the Problem Solving forum “$$?\,\,\,:\,\,\,{\rm{approx}}.\,\,{\rm{degrees - rotation}}\,\,\,{\rm{in}}\,\,\,{\rm{1}}\,\,{\rm{min}}360\,\,{\rm{degrees - rotation}}\,\,\,\, \leftrightarrow \,\,\,\,2 \cdot \pi \cdot 300\,\,{\rm{meters}}\,\,\,\,\,\,\left( {1\,\,{\rm{lap}}} \right)10\,\,{\rm{meters}}\,\,\,\, ...” February 22, 2019 fskilnik@GMATH posted a reply to The curve shown above is defined by the ordered-pairs (x,y) in the Problem Solving forum “$$y = A{x^2} + 2Bx + C$$ $$A > 0\,\,:\,\,\,{\rm{parabola}}\,\,{\rm{concave}}\,\,{\rm{upward}}\,$$ $$C > 0\,\,:\,\,\,y - {\rm{intercept}}\,\,{\rm{ > }}\,\,{\rm{0}}\,\,\,\,\,\,\,\,\leftThe correct answer is (C). We follow the notations and rationale taught in the GMATH method. ...” February 22, 2019 Brent@GMATPrepNow posted a reply to Last year the range of the annual salaries of the 100 in the Problem Solving forum “A quick solution is to assign some values to the highest paid and lowest paid workers Let 10,000 = the lowest salary LAST YEAR Let 40,000 = the highest salary LAST YEAR This satisfies the condition that the range LAST YEAR = 30,000 If the annual salary of each of the 100 employees this ...” February 21, 2019 Brent@GMATPrepNow posted a reply to The sum of two integers is 27. The larger integer is 25% in the Problem Solving forum “Let x = the smaller integer So, 1.25x = the larger integer (since the larger integer is 25% greater than the smaller integer) The sum of two integers is 27. We can write: x + 1.25x = 27 Simplify: 2.25x = 27 Solve: x = 27/2.25 IMPORTANT: What''s a nice fast way to evaluate 27/2.25? An easy ...” February 21, 2019 fskilnik@GMATH posted a new topic called Brenda will test-drive a vintage motor car on a circular tra in the Problem Solving forum “GMATH practice exercise (Quant Class 5) Brenda will test-drive a vintage motor car on a circular track with radius 300 meters, at a constant speed of 10 meters per second. If her husband Jim is at rest, at the center of this track, to film the entire test-drive, which of the following values is ...” February 21, 2019 fskilnik@GMATH posted a new topic called In the figure shown, AB = AC = 12. Which of the following is in the Problem Solving forum “GMATH practice exercise (Quant Class 7) https://i.ibb.co/XyZrzVC/21-Feb19-7k.gif In the figure shown, AB = AC = 12. Which of the following is closest to the area of the circle with center O that is tangent, at points M, N, and P, to the circular sector ABPC with center A and central angle of ...” February 21, 2019 fskilnik@GMATH posted a new topic called The curve shown above is defined by the ordered-pairs (x,y) in the Problem Solving forum “GMATH practice exercise (Quant Class 13) https://i.ibb.co/yQqt4tj/21-Feb19-4p.gif The curve shown above is defined by the ordered-pairs (x,y) such that y = f(x) = Ax^2+2Bx+C, where A, B and C are given constants. If the point of tangency with the x-axis has a positive x-coordinate, which of ...” February 21, 2019 Brent@GMATPrepNow posted a reply to What is the greatest positive three-digit number that is div in the Problem Solving forum “One approach is to check each answer choice, beginning with the largest answer choice E. 840 840 is divisible by 2, 3, 4, 5, 6 and 7 Answer: E Cheers, Brent” February 21, 2019 Brent@GMATPrepNow posted a reply to What is the largest digit n for which the number 123,45n is in the Problem Solving forum “RULE: if the SUM of the digits of a number is divisible by 3, then that number is divisible by 3 Take, for example, the number 1,001,226 1 + 0 + 0 + 1 + 2 + 2 + 6 = 12 Since 12 is divisible by 3, we know that 1,001,226 is divisible by 3 If 123,45n is divisible by 3, then 1 + 2 + 3 + 4 + 5 + n ...” February 21, 2019 fskilnik@GMATH posted a new topic called The graphs of the functions f and g are represented in In th in the Problem Solving forum “GMATH practice exercise (Quant Class 20) https://i.ibb.co/3TSJ3Sf/21-Feb19-3z.gif The graphs of the functions f and g are represented in In the figure given. If f(x) = c^x (c constant), what is the value of g(g(-1)+1) + f(g(3)+1)? (A) 4 (B) 5 (C) 6 (D) 7 (E) 8 Answer: ____(E)__” February 21, 2019 Brent@GMATPrepNow posted a reply to In the figure above, the angle marked at c has been created in the Data Sufficiency forum “Target question: What is the sum of a, b, and c? This is a good candidate for rephrasing the target question. Since angles on a line add to 180°, we already know that b + c = 180 We get: a + b + c = a + 180 So, in order to find the sum of a, b and c, we need only find the value of a ...” February 21, 2019 Brent@GMATPrepNow posted a reply to At a certain committee meeting only associate professors and in the Problem Solving forum “Notice that the question asks us to find that TOTAL number of people present. In other words, it the question does NOT ask us to find the number of associate professors or assistant professors present. Since each person brings THREE items, and since total of 21 items were brought (10 pencils ...” February 21, 2019 Brent@GMATPrepNow posted a reply to In a class of 30 students, 2 students did not borrow any in the Problem Solving forum “The average (arithmetic mean) number of book borrowed per student was 2. Since there are 30 students altogether, the total number of borrowed books = (2)(30) = 60 2 students borrowed 0 books: total of 0 books 12 students borrowed 1 book each: total of 12 books 10 students borrowed 2 books ...” February 21, 2019 Brent@GMATPrepNow posted a reply to If there are more than two numbers in a certain list, is in the Data Sufficiency forum “Target question: Is each of the numbers n the list equal to zero? Given: There are more than 2 numbers in the list Statement 1: The product of any 2 numbers in the list is ZERO There are several possible sets that satisfy this condition. Here are two: Case a: the set is {0, 0, 0} in ...” February 21, 2019 fskilnik@GMATH posted a reply to A box has only pure material A identical coins, pure materia in the Data Sufficiency forum “$$\left. \matrix{ {\rm{A}}\,\,{\rm{coins}}\,\,{\rm{material}}\,\,{\rm{A}}\,\,\, \to \,\,\,\$ x\,\,{\rm{worth}}\,\,{\rm{each}} \hfill \cr {\rm{B}}\,\,{\rm{coins}}\,\,{\rm{material}}\,\,{\rm{B}}\,\,\, \to \,\,\,\\$ y\,\,{\rm{worth}}\,\,{\rm{each}} \hfill \cr ...”
February 20, 2019
fskilnik@GMATH posted a reply to What is the value of the positive two-digit integer N? in the Data Sufficiency forum
“$$? = N = \left\langle {ab} \right\rangle \,\,\,\,\,\,\,\left We follow the notations and rationale taught in the GMATH method. Regards, Fabio. P.S.: we know 28 and 39 could be found by some "organized manual work"... but the importance of the solution is contained in the ...” February 20, 2019 fskilnik@GMATH posted a reply to A number is called "mystic" if it can be expressed in the Problem Solving forum “$$?\,\,\,:\,\,\,M + \left( {M + 1} \right) + \left( {M + 2} \right) + \ldots + NM \ge 2N > 2M\,\,\,\,\,\leftYES, this is a very hard problem, but I believe many "pieces" of this solution are VERY useful for candidates aiming really outstanding performances! We follow ...”
February 20, 2019
fskilnik@GMATH posted a reply to Four cards are chosen from a standard deck: two aces (one of in the Problem Solving forum
“$$\left\{ { - 2, - 1,1,2} \right\}\,\, \to \,\,{\rm{two}}\,{\rm{different}}\,\,{\rm{chosen}}$$ $$? = P\left( {{\rm{odd}}\,\,{\rm{or}}\,\,{\rm{negative}}\,\,{\rm{product}}} \right)$$ $${\rm{6}}\,\,{\rm{equiprobable}}\,\,{\rm{outcomes}}\,\,:\,\,\,\left\{ \matrix{ \,\left\{ { - 2, - 1} ...” February 20, 2019 fskilnik@GMATH posted a reply to The product of three different numbers is greater than 1000. in the Data Sufficiency forum “$$a < b < cabc > 1000? = c\left( 1 \right)\,\,{\rm{primes}}\,\,\,\left\{ \matrix{ \,{\rm{Take}}\,\,\left( {a,b,c} \right) = \left( {7,11,13} \right)\,\,\,\,\leftGMATH method. Regards, Fabio.”
February 20, 2019
fskilnik@GMATH posted a reply to Each student in a certain class is considered intermediate o in the Problem Solving forum
“https://i.ibb.co/MnVZF7c/19-Feb19-6j.gif $$?\,\, = \,\,\frac{{100}}{{100 + x}}$$ $$\left( {{\text{Alligation}}} \right)\,\,\,\,?\,\, = \,\,\frac{{100}}{{100 + x}}\,\, = \,\,\frac{{5.8 - 4.3}}{{6.3 - 4.3}}\,\, = \,\,\frac{{1.5}}{2}\,\, = \,\,\underleftrightarrow {\frac{1}{{10}}\left( ...” February 20, 2019 fskilnik@GMATH posted a reply to The graphs of y=7x+1 and y=kx^3 are represented in the figur in the Problem Solving forum “https://i.ibb.co/D8FnRQp/19-Feb19-5w.gif$$? = mC = \left( {c,8} \right) \in {\rm{line}}\,\,\,\,\, \Rightarrow \,\,\,\,\,8 = 7 \cdot c + 1\,\,\,\,\, \Rightarrow \,\,\,\,\,c = 1C = \left( {c,8} \right) = \left( {1,8} \right) \in {\rm{cubic}}\,\,\,\,\, \Rightarrow \,\,\,\,\,8 = k \cdot ...”
February 20, 2019
fskilnik@GMATH posted a new topic called A box has only pure material A identical coins, pure materia in the Data Sufficiency forum
“GMATH practice exercise (Quant Class 14) A box has only pure material A identical coins, pure material B identical coins, and pure material C identical coins. Each coin is worth a certain integral number of dollars and coins of different materials don´t have the same dollar value. What is the ...”
February 20, 2019
Brent@GMATPrepNow posted a reply to Is mn < 10? in the Data Sufficiency forum
“Target question: Is mn < 10? Statement 1: m < 5 and n < 2 Let''s TEST some values. There are several values of m and n that satisfy statement 1. Here are two: Case a: m = 0 and n = 0. In this case mn = (0)(0) = 0. So, the answer to the target question is YES, mn IS less than 10 ...”
February 20, 2019
fskilnik@GMATH posted a new topic called Four cards are chosen from a standard deck: two aces (one of in the Problem Solving forum
“GMATH practice exercise (Quant Class 19) Four cards are chosen from a standard deck: two aces (one of Spades, another of Hearts) and two kings (one of Spades, another of Hearts). The aces are considered as -1 (Spades) and 1 (Hearts), while the kings are considered as -2 (Spades) and 2 (Hearts). ...”
February 20, 2019
fskilnik@GMATH posted a new topic called What is the value of the positive two-digit integer N? in the Data Sufficiency forum
“GMATH practice exercise (Quant Class 16) What is the value of the positive two-digit integer N? (1) N and the product of the digits of N are 12 units apart. (2) N is greater than the product of the digits of N. Answer: ____(E)__”
February 20, 2019
fskilnik@GMATH posted a new topic called The product of three different numbers is greater than 1000. in the Data Sufficiency forum
“GMATH practice exercise (Quant Class 16) The product of three different numbers is greater than 1000. What is the value of the largest among them? (1) The numbers are primes. (2) The product of the numbers is less than 1310. Answer: ___(E)__”
February 20, 2019
Brent@GMATPrepNow posted a reply to Bite-sized video lessons from GMAT Prep Now in the GMAT Math forum
“Data Sufficiency lesson #4: GMAT Data Sufficiency Strategies - Part I Video : https://www.youtube.com/watch?v=Ep09hi1OJpI Cheers, Brent”
February 20, 2019
Brent@GMATPrepNow posted a reply to John takes 15 hours to complete a certain job, while Bill ta in the Problem Solving forum
“Let''s first see what happens if Steven works as fast as possible. Since Bill can complete the job in 6 hours, Steven must complete the job in a little more than 6 hours. For example, we COULD see what happens if Steven takes 6.000000000000001 hours to complete the job. Unfortunately, ...”
February 20, 2019
Brent@GMATPrepNow posted a reply to If x, y, and z are three-digit positive integers and if x = in the Data Sufficiency forum
“Target question: Is the hundreds digit of x equal to the sum of the hundreds digits of y and z ? Notice that there are essentially 3 ways for the hundreds digit of x to be different from the sum of the hundreds digits of y and z Scenario #1: the hundreds digits of y and z add to more than 9. ...”
February 20, 2019
fskilnik@GMATH posted a reply to A square has an area of (0.027)^(-2/3) square meters. The pe in the Problem Solving forum
“$$? = 4L$$ $${L^2} = {\left( {{3^3} \cdot {{10}^{ - 3}}} \right)^{ - {2 \over 3}}} = {\left We follow the notations and rationale taught in the GMATH method. Regards, Fabio.” February 20, 2019 fskilnik@GMATH posted a reply to A square has an area of (0.027)^(-2/3) square meters. The pe in the Problem Solving forum “$$? = 4L{L^2} = {\left( {{3^3} \cdot {{10}^{ - 3}}} \right)^{ - {2 \over 3}}} = {\left We follow the notations and rationale taught in the GMATH method. Regards, Fabio.”
February 20, 2019
fskilnik@GMATH posted a new topic called Each student in a certain class is considered intermediate o in the Problem Solving forum
“GMATH practice exercise (Quant Class 6) Each student in a certain class is considered intermediate or strong, but not both. The average of the grades of the strong students is 6.3 points, exactly two points above the average of the grades of the intermediate students. What is the percentage of ...”
February 19, 2019
fskilnik@GMATH posted a new topic called A square has an area of (0.027)^(-2/3) square meters. The pe in the Problem Solving forum
“GMATH practice exercise (Quant Class 12) A square has an area of (0.027)^(-2/3) square meters. The perimeter of this square, in meters, belongs to which of the following intervals? (A) ___(D)__”
February 19, 2019
fskilnik@GMATH posted a new topic called The graphs of y=7x+1 and y=kx^3 are represented in the figur in the Problem Solving forum
“GMATH practice exercise (Quant Class 13) https://i.ibb.co/f4YTfhw/19-Feb19-3w.gif The graphs of y=7x+1 and y=kx^3 are represented in the figure shown (k is a constant). If line AB is parallel to the x-axis, what is the abscissa (x-coordinate) of point B? (A) 1 (B) 0.75 (C) 0.5 (D) 0.25 ...”
February 19, 2019
fskilnik@GMATH posted a reply to Three points are randomly chosen on the circumference of a g in the Problem Solving forum
“We will refer to the link given in the hint: https://www.beatthegmat.com/three-points-are-chosen-independently-an-at-random-on-the-ci-t306462.html#826897 https://i.ibb.co/5nBHyTN/18-Feb19-5z.gif FOCUS: P(center inside the triangle) We may consider (without loss of generality) that the ...”
February 19, 2019
fskilnik@GMATH posted a reply to Is the x-intercept of the non-horizontal line L negative? in the Data Sufficiency forum
“$$c = {\left( {x - {\rm{intercept}}} \right)_{\rm{L}}}\,\,\mathop {\rm{ < }}\limits^? \,\,{\rm{0}}$$ $$L\,\,\,:\,\,\,{\rm{vertical}}\,\,{\rm{or}}\,\,{\rm{non - vertical}}\,\,{\rm{with}}\,\,m = {\rm{slop}}{{\rm{e}}_{\rm{L}}} \ne 0$$ $$\left( 1 \right)\,\,\,L\,\,{\rm{non - ...” February 19, 2019 Brent@GMATPrepNow posted a reply to George bought a large electronic item with a 15% off coupon in the Problem Solving forum “George was SUPPOSED to receive a 15% discount, but he received a 30% discount. So, he should have returned 15% of the original cost. However, the manager asked for half that amount (i.e., 7.5% of the original cost) In other words, 7.5% of the original cost = 40.50 IMPORTANT: at this point, ...” February 19, 2019 fskilnik@GMATH posted a new topic called A number is called \"mystic\" if it can be expressed as the su in the Problem Solving forum “GMATH practice exercise (Quant Class 17) A number is called "mystic" if it can be expressed as the sum of at least three consecutive positive integers greater than 1, in which the larger addend is more than twice the smaller addend. Note that 25 (=3+4+5+6+7) and 44 (=2+3+4+5+6+7+8+9) ...” February 19, 2019 fskilnik@GMATH posted a reply to If M, N are integers greater than 1 such that 2M<N, which in the Problem Solving forum “Although the problem seems hard, the focused-numbers (half the numbers given) are SMALL... and that´s the hint to try some "organized manual work"! We are looking for the 25 (III), 26 (II) and 27 (I) possibilities.$${S_K} = 1 + 2 + \ldots + K = {{K\left( {K + 1} \right)} \over ...”
February 19, 2019