If 3

Question

If 3 < X < 5 and 8 < Y < 11, then which of the following options is TRUE?

A. (3/11)(Y/X) < 1
B. (3/8)(Y/X) > 1
C. (3/5)(Y/X) < 1
D. (3/8)(Y/X) < 1

Accepted Answer

B. (3/8)(Y/X) > 1 We need to determine which of the four statements holds for every allowed pair (X, Y). The approach is to find the tightest guaranteed lower bound for Y/X, then check which multiplier makes the product definitely exceed 1. Since Y > 8 and X < 5, the product (8/5)(Y/X) has its minimum just above 8/5 * (8/5) which exceeds 1 when the coefficient is at least 5/8.

If 3 < X < 5 and 8 < Y < 11, then which of the following options is TRUE? A. (3/11)(Y/X) < 1 B. (3/8)(Y/X) > 1 C. (3/5)(Y/X) < 1 D. (3/8)(Y/X) < 1