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## Integers a and b are such that a -b...

This topic has 1 expert reply and 0 member replies

### Top Member

Vincen Legendary Member
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#### Integers a and b are such that a -b...

Tue Sep 12, 2017 11:18 am
Integers a and b are such that a - b > 0. Is |a| > |b| ?

(1) ab > 0
(2) a + b = 12

The OA is B.

Why is B the answer?

### GMAT/MBA Expert

Jay@ManhattanReview GMAT Instructor
Joined
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Tue Sep 19, 2017 4:31 am
Vincen wrote:
Integers a and b are such that a - b > 0. Is |a| > |b| ?

(1) ab > 0
(2) a + b = 12

The OA is B.

Why is B the answer?
Given that a - b > 0 => a > b.

We have to determine whether |a| > |b|.

Statement 1: ab > 0

=> Either a and b both are positive or both are negative.

Case 1: Say a = 3 and b = 2 (a > b), then |3| > |2|. The answer is Yes.
Case 2: Say a = -2 and b = -3 (a > b), then |-2| < |-3| => 2 < 3. The answer is No.

Insufficient.

Statement 2: a + b = 12

Had a = b, then a = b = 6. But we know that a > b, thus a > 6 and b < 6. This means that |a| > |b|. Sufficient.

If you try to increase the value of |b| so that it may be greater than |a|, it is not possible.

Say b = -10, thus |b| = 10.

From a + b = 12, we get a +(-10) = 12 => a - 10 = 12 => a = 22.

Thus, |a| > |b|. The answer is Yes.

The correct answer: B

Hope this helps!

Download free ebook: Manhattan Review GMAT Quantitative Question Bank Guide

-Jay
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