If a and b are negative numbers, is b > a ?
(1) a/b > 1
(2) b/a < 1
Answer: D
Source: GMAT prep
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If a and b are negative numbers, is b > a ?
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BTGModeratorVI
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Given: a and b are NEGATIVE numbersBTGModeratorVI wrote: ↑Thu Aug 20, 2020 7:12 amIf a and b are negative numbers, is b > a ?
(1) a/b > 1
(2) b/a < 1
Answer: D
Source: GMAT prep
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
Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
We can multiply the inequality in Statement 1 by \(b\) on both sides, reversing the inequality because \(b\) is negative, to find thatBTGModeratorVI wrote: ↑Thu Aug 20, 2020 7:12 amIf a and b are negative numbers, is b > a ?
(1) a/b > 1
(2) b/a < 1
Answer: D
Source: GMAT prep
\(a < b\) 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
