DH99 wrote:

If x and y are nonzero integers such that -12≤ x ≤ 1 and -4≤ y ≤10, what is the sum of the minimum and the maximum possible values of x/y?

A. -8

B. -4

C. 0

D. 4

E. 8

Since both x and y can be positive or negative, we see that the maximum possible value of x/y is one such that x and y have the same sign (so that x/y is positive) and the minimum possible value of x/y is one such that x and y have opposite signs (so that x/y is negative). With that in mind, let’s determine the maximum possible value of x/y.

If we want x/y to be maximum, and both x and y are positive, we want both x and y to be equal to 1, so that x/y = 1. If both x and y are negative, we want x to be -12 and y to be -1, so that x/y = 12. Thus, the maximum value of x/y is 12.

Now let’s determine the minimum possible value of x/y.

If we want x/y to be a minimum, and x is positive and y is negative, we want x to be 1 and y to be -1, so that x/y = -1. If x is negative and y is positive, we want x to be -12 and y to be 1, so that x/y = -12. Thus, the minimum value of x/y is -12.

We see that the sum of the minimum and the maximum possible values of x/y is -12 + 12 = 0.

Answer: C

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