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A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
35%
(medium)
Question Stats:
69% (01:13) correct
31%
(01:25)
wrong
based on 48
sessions
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Is \(x > y\) ?
(1) \((x – y)^3 > (x – y)^2\)
(2) \((x – y)^4 > (x – y)^3\)
(1) \((x – y)^3 > (x – y)^2\)
(2) \((x – y)^4 > (x – y)^3\)
Updated on: 17 May 2021, 07:43
Originally posted by BrentGMATPrepNow on 19 Mar 2020, 06:46.
Last edited by BrentGMATPrepNow on 17 May 2021, 07:43, edited 1 time in total.
Last edited by BrentGMATPrepNow on 17 May 2021, 07:43, edited 1 time in total.
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Bunuel
Target question: Is \(x > y\)
Statement 1: \((x – y)^3 > (x – y)^2\)
From this information, we can conclude that (x - y) does not equal zero
This means that (x - y)² must be POSITIVE, which means we can safely take \((x – y)^3 > (x – y)^2\) and divide both sides by (x - y)²
When we do so, we get: x - y > 1
If x - y > 1, we can also conclude that x - y > 1 > 0
If x - y > 0, we can add y to both sides to get x > y
The answer to the target question is YES, it's the case that x > y
Since we can answer the target question with certainty, statement 1 is SUFFICIENT
Statement 2: \((x – y)^4 > (x – y)^3\)
In this case it might be tempting to use the same strategy we used for statement 1 and divide both sides of the inequality by (x - y)³
The problem with this approach is that we don't know whether (x - y)³ is positive or negative.
Consider these two conflicting cases (both of which satisfy statement 2):
Case a: x = 2 and y = 0. In this case, the answer to the target question is YES, it's true that x > y
Case b: x = 0 and y = 2. In this case, the answer to the target question is NO, it's not the case that x > y
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT
Answer: A
Cheers,
Brent
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10 May 2021, 10:53
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