AAPL wrote:If x and y are integers and |x - y| = 12, what is the minimum possible value of xy?
A. -12
B. -18
C. -24
D. -36
E. -48
We see that all the answer choices are negative; thus, one of the values of x and y must be negative and the other positive. We can let x be negative, and y be positive.
If x = -1, then y = 11 and xy = -11.
If x = -2, then y = 10 and xy = -20.
If x = -3, then y = 9 and xy = -27.
If x = -4, then y = 8 and xy = -32.
If x = -5, then y = 7 and xy = -35.
If x = -6, then y = 6 and xy = -36.
If x = -7, then y = 5 and xy = -35.
We can stop here since we see that we have the minimum product of -36 when x = -6 and y = 6. (Note: Had we continued, the product will be increasing rather than decreasing since the product will be a mirror image of what we have. That is, after the last product -35, the subsequent ones will be -32, -27, -20 and -11.)
Answer: D
