If \(a\) and \(b\) are negative numbers, is \(b > a ?\)

[M7MBA]

If \(a\) and \(b\) are negative numbers, is \(b > a ?\)

(1) \(\dfrac{a}{b} > 1\)
(2) \(\dfrac{b}{a} < 1\)

[spoiler]OA=D[/spoiler]

Source: GMAT Prep

[Brent@GMATPrepNow]

If \(a\) and \(b\) are negative numbers, is \(b > a ?\)

(1) \(\dfrac{a}{b} > 1\)
(2) \(\dfrac{b}{a} < 1\)

[spoiler]OA=D[/spoiler]

Source: GMAT Prep

Given: a and b are NEGATIVE numbers

IMPORTANT CONCEPT: If we divide both sides of an inequality by a NEGATIVE value, we must REVERSE the direction of the inequality sign.

Target question: Is b > a ?

Statement 1: a/b > 1
Multiply both sides of the inequality by b to get: a < b (notice that we REVERSED the direction of the inequality sign)
The answer to the target question is YES, it is true that b > a
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: b/a < 1
Multiply both sides of the inequality by a to get: b > a (notice that we REVERSED the direction of the inequality sign)
The answer to the target question is YES, it is true that b > a
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer: D

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