If x and y are integers and |x - y| = 10, what is the minimum possible value of xy?  Choices.
A) -9 B) -18 C) -24 D) -25 E) -48
Sometimes the answer choices to a given question provide a big 'hint' as to how you can go about solving it. This prompt can also be solved without any complex math ideas - you just need to do a bit of 'brute force' math and you'll have the answer relatively quickly.   We're told that X and Y are INTEGERS and |X - Y| = 10. We're asked for the MINIMUM possible value of (X)(Y).   Since all of the answer choices are NEGATIVE, this tells us that ONE of the two variables MUST be negative (and the other must be positive), so we should restrict our work to those options.   IF...   X = 9, Y = -1, then XY = -9   X = 8, Y = -2, then XY = -16   X = 7, Y = -3, then XY = -21   X = 6, Y = -4, then XY = -24   X = 5, Y = -5, then XY = -25   X = 4, Y = -6, then XY = -24   X = 3, Y = -7, then XY = -21   From this, we can conclude the XY will start to get bigger as X continues to decrease down to 1, so there's no need to do any additional work.   Final Answer:   -25
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If x and y are integers and |x - y| = 10, what is the minimum possible value of xy?