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DS Question Inequalities

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by vinay1983 » Thu Sep 05, 2013 2:17 am
Is 1/(a-b) < b-a?

(1) a < b
(2) 1 < la-bl (modulus a-b)
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Source: — Data Sufficiency |
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by ganeshrkamath » Thu Sep 05, 2013 2:56 am
vinay1983 wrote:Is 1/(a-b) < b-a?

(1) a < b
(2) 1 < la-bl (modulus a-b)
Statement 1: a < b
(a-b) < 0 and (b-a) > 0
The question becomes
1/negative < positive?
Sufficient.

Statement 2:
Two cases:
Case 1: (a-b) > 1
Case 2: (a-b) < -1
We get a NO for Case 1 and a YES for Case 2.
Not sufficient.

Choose A

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by Brent@GMATPrepNow » Thu Sep 05, 2013 6:12 am
vinay1983 wrote:Is 1/(a-b) < b-a?

(1) a < b
(2) 1 < |a-b|
Note: My solution is very similar to ganeshrkamath's, but mine uses specific values for a and b in statement 2.


Target question: 1/(a-b) < b-a?

Statement 1: a < b
From this, we can conclude that a-b is negative, and a+b is positive
So, the question becomes: Is 1/negative < positive?, and the answer is a resounding YES!
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: 1 < |a-b|
There are several values of a and b that satisfy this condition. Here are two:
Case a: a = -2 and b = 0, in which case 1/(a-b) < b-a
Case b: a = 2 and b = 0, in which case 1/(a-b) > b-a
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Answer = A

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