Bunuel wrote:

If x^2 + xy - 32 = 0, and x and y are integers, then y could equal each of the following except?

A) -31

B) -14

C) 2

D) 4

E) 14

We can express the equation as follows:

x(x + y) = 32

Since x and y are integers, x and x + y are integer factors of 32. For example, if x = 4, then x + y = 8 which makes y = 4. So choice D is not the answer.

If x = -1, then x + y = -32 which makes y = -31. So choice A is not the answer.

If x = -2, then x + y = -16 which makes y = -14. So choice B is not the answer.

If x = 2, then x + y = 16 which makes y = 14. So choice E is not the answer.

Answer: C

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