Given that 0 < a < 1 < b < 3, which of the following must be less than 1?
I. a/b
II. ab
III. b - a

Answer Choices

Correct answer marked below

I only

Correct

II Only

III Only

I and II

I and III

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Explanation

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Official Explanation

Official

Since 0 < a < 1 and 1 < b < 3, we analyze each option. For I, since a is less than 1 and b is greater than 1, the fraction a/b will be less than 1. For II, the product…

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Comments

YousraMar 20, 2025

Can you explain more?

AshFeb 16, 2024

Great

What this question tests

What it tests

Your ability to solve and combine linear inequalities and reason about ranges of values.

Common trap

Failing to flip the inequality sign when multiplying or dividing by a negative, or missing an inclusive/exclusive endpoint.

Given that 0 < a < 1 < b < 3, which of the following must be less than 1? I. a/b II. ab III. b - a