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
III Only
I and II
I and III

Solution:

Given, 0 < r < 1 and 0 < s < 2

Here both are positive numbers and r < s

(i) r/s

Let us take r = 1 and s = 1.75

r/s = 1/1.75 = 0.57

r/s < 1

(ii) r.s

Case 1 : Let us take r = 0.95 and s = 1.9

r × s = 0.95 × 1.9 = 1.805 ＞1

Case 2 : Let us take r = 0.5 and s = 1.5

r × s = 0.5 × 1.5 = 0.75 < 1

(iii) s - r

Let us take s = 1.9 and r = 0.5

s - r = 1.9 - 0.5 = 1.4

s - r ＞1

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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 III Only I and II I and III

Summary:

If 0 < r < 1 < s < 2, r/s will always be less than 1. We have also observed that s - r ＞1.