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If a and b are negative numbers, is b > a ?

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Source: — Data Sufficiency |

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Re: If a and b are negative numbers, is b > a ?

by Brent@GMATPrepNow » Tue Aug 25, 2020 9:08 am
BTGModeratorVI wrote: ↑
Thu Aug 20, 2020 7:12 am
 If a and b are negative numbers, is b > a ?

(1) a/b > 1
(2) b/a < 1

Answer: D
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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Re: If a and b are negative numbers, is b > a ?

by swerve » Tue Aug 25, 2020 1:04 pm
BTGModeratorVI wrote: ↑
Thu Aug 20, 2020 7:12 am
 If a and b are negative numbers, is b > a ?

(1) a/b > 1
(2) b/a < 1

Answer: D
Source: GMAT prep
We can multiply the inequality in Statement 1 by \(b\) on both sides, reversing the inequality because \(b\) is negative, to find that

\(a < b\) hence Statement 1 is sufficient. \(\Large{\color{green}\checkmark}\)

We can multiply the inequality in Statement 2 by \(a\) on both sides, reversing the inequality because \(a\) is negative, to find that

\(b > a\) so Statement 2 is also sufficient. \(\Large{\color{green}\checkmark}\)

Therefore, the correct answer is D
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