2012-03-16 09:00:46

x and y are integers where x < 0 < y. If |x - 3| < 4 and |y| < 6, what is the maximum value |xy| could be?

The correct answer is 30

Explanation: Since the question asks for the maximum value of a quantity, try to find the maximum values of x and y. The absolute value of xy will always be positive, so x or y could be negative numbers of positive numbers. If |y| < 6, then  -y < 6 or y < 6. Since y has to be an integer, y could be no higher than 5. If |x - 3| < 4, then x - 3 < 4 and -(x - 3) < 4. These require some work to simplify:

x - 3 < 4 simplifes to x < 7 (from adding 3 to both sides of the inequality).

-(x - 3) < 4 simplifies to x > -1 (the first step is to divide both sides by -1, which flips the < sign; after that, add 3 to both sides to get x > -1). This means x has to be between -1 and 7 to hold true, meaning the maximum value x could be is 6.

6 x 5 = 30, so the maximum value of |xy| is 30.