jmc

Question

Let a and b be real numbers. Consider the following five statements: 1a < 1b a^2 > b^2 a < b a < 0 b < 0 What is the maximum number of these statements that can be true for any values of a and b?

Accepted Answer

Suppose a < 0, b < 0, and a < b. Then 1a - 1b = b - aab > 0,so 1a > 1b. Thus, not all five statements can be true. If we take a = -2 and b = -1, then all the statements are true except the first statement. Hence, the maximum number of statements that can be true is 4.