If x and y are integers and |x-y|=12, what is the minimum

Hi AAPL,

We're told that X and Y are integers and |X - Y| = 12. We're asked for the MINIMUM possible value of (X)(Y). You will likely find that a bit of 'brute force' Arithmetic is the easiest way to get to the correct answer.

To start, ALL of the answers are NEGATIVE, which means that one of the variables will be POSITIVE and the other will be NEGATIVE.

IF....
X = 11 and Y = -1, then the product is -11
X = 10 and Y = -2, then the product is -20
X = 9 and Y = -3, then the product is -27
X = 8 and Y = -4, then the product is -32
X = 7 and Y = -5, then the product is -35
X = 6 and Y = -6, then the product is -36
X = 5 and Y = -7, then the product is -35

From here, the products will follow the above pattern, but in reverse. Thus, the minimum possible product is -36.

Final Answer: D

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Rich

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