Given that ab > 0 and ac < 0, which of the following statements must hold true?
I. b/c < 0
II. abc < 0
III. ab - ac > 0

Answer Choices

Correct answer marked below

I only

III only

I and II

I and III

Correct

II and III

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Official Explanation

Official

Since ab > 0, it indicates that either both a and b are positive or both a and b are negative. The condition ac < 0 implies that a and c must have opposite signs. If a is positive, then c must be negative, and if a is negative, then c must be positive. I. The statement b/c < 0 must be true because b and a share the same sign, while a and c have opposite signs. Therefore, b and c must also have opposite signs, leading to b/c < 0. II. The statement abc < 0 is not necessarily true in all cases. For…

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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 ab > 0 and ac < 0, which of the following statements must hold true? I. b/c < 0 II. abc < 0 III. ab - ac > 0