Problem Solving

AAPL wrote:If 0 < r < 1 < s < 2, which of the following must be less than 1?

I. r/s
II. rs
III. s - r

A. I only
B. II only
C. III only
D. I and II
E. I and III

We are given that 0 < r < 1 < s < 2 and need to determine which Roman Numeral expressions must be less than 1. Let's test each expression.

I. r/s

Since r is less than s and both r and s are positive, r/s will always be less than 1. Roman numeral I is correct.

II. rs

The product of r and s does not have to be less than 1. For example, if r = 0.8 and s = 1.5 the product of r and s will be (0.8)(1.5) = 1.2, which is greater than 1. Roman numeral II is not correct.

III. s - r

s - r does not have to be less than 1. For example, if s = 1.9 and r = 0.1, s - r = 1.8. Roman number III is not correct.

Answer: A