Each question is in this format
<start>Question: --QUESTION--
Choices : --A--, --B--, --C--, --D--
Planning For Answer: --PLAN FOR ANSWER--
Answer key: "--LETTER--"<end>

<start>Question: Find the degree for the given field extension Q(sqrt(2), sqrt(3), sqrt(18)) over Q.
Choices : "0", "4", "2", "6"
Planning For Answer: The field Q(sqrt(2), sqrt(3), sqrt(18)) is an extension field of Q that includes the square roots of 2, 3, and 18. Notice that sqrt(18) = sqrt(2*9) = sqrt(2)sqrt(9) = 3sqrt(2), so sqrt(18) can be expressed in terms of sqrt(2), which means that including sqrt(18) in the field doesn't actually increase the degree of the extension.
Thus, the field Q(sqrt(2), sqrt(3), sqrt(18)) is the same as the field Q(sqrt(2), sqrt(3)).
For the degree of a simple extension field Q(a, b) over Q, we want to find the least common multiple (lcm) of the degrees of the extension fields Q(a) over Q and Q(b) over Q.
sqrt(2) and sqrt(3) are both irrational numbers, and the minimal polynomials that they are roots of are both quadratic (x^2 - 2 and x^2 - 3, respectively). Thus, the extension fields Q(sqrt(2)) and Q(sqrt(3)) are both of degree 2 over Q.
Therefore, the field Q(sqrt(2), sqrt(3)) has degree lcm(2, 2) = 2 * 2 = 4 over Q. The square root of 18 does not increase the degree of the field, as explained above.
So, the field Q(sqrt(2), sqrt(3), sqrt(18)) also has degree 4 over Q.
Answer key: "B"<end>

<start>Question: NAME_1 is five years older than NAME_2, who is twice NAME_3's age at seven.  Calculate NAME_1's age.
Choices : "14", "7", "21", "19"
Planning For Answer: Given that NAME_2 is twice NAME_3's age, and NAME_3 is seven years old, NAME_2 would be 2 * 7 = 14 years old. Since NAME_1 is five years older than NAME_2, NAME_1 would be 14 + 5 = 19 years old.
Answer key: "D"<end>

<start>Question: ['Use the expression below to answer the question. 3 × [(2 × 6 – 5) + (8 ÷ 4)] – 1 What is the value of the expression?']
Choices: ['9'], ['11'], ['26'], ['32']
Planning For Answer: To answer this question Wrap the entire output in JSON format.
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