Is 1/(a - b) > b - a ? (1) a < b (2) 1 < |a - b| GMAT Data Sufficiency

Question: Is 1/(a - b) > b - a ?

1. a < b
2. 1 < |a - b|

1. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.        
2. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.        
3. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.        
4. EACH statement ALONE is sufficient.        
5. Statements (1) and (2) TOGETHER are not sufficient.

Correct Answer: A

Solution and Explanation
Approach Solution 1:
The given condition for the problem states that 1/(a - b) > b - a which needs to be proved. Accordingly, two statements have been given that need to be identified whether being sufficient or not.

The first statement is a < b which implies that a - b < 0 stating that the Left hand Side (LHS) is negative. While on the other hand, if b - a > 0 then the Right Hand Side (RHS) becomes positive. Hence, it proves that negative < positive hence, the statement is sufficient.

The second statement states that 1 < |a - b|. This implies that if a−b=2a−b=2 then LHS>0 and RHS<0. Further, in this case the answer will be yes if a−b=−2a−b=−2 then LHS<0 and RHS>0 and in this case the answer will be no. Hence, the statement is not sufficient for 1/(a - b) > b - a.

Approach Solution 2:
The given case states that 1/(a - b) > b - a
In order to understand if this can be proved, the following two statements are to be proved sufficient or insufficient.

Accordingly, the first statement states that-
=> a < b
=> a-b<0, implying that b-a > 0.
To understand whether 1/negative < positive, it proves that yes, this is sufficient.

The second statement states that 1 < |a - b|
Accordingly, it’s possible that a-b = 2, implying that b-a = -2.
Plugging a-b=2 and b-a=-2 into 1/(a-b) < b-a, we get:
1/2 < -2

Hence, this statement is not sufficient.

Approach Solution 3:
Statement 1: a < b
Thus, a-b<0, implying that b-a>0.
Is 1/(negative) < positive?
YES.
SUFFICIENT.

Statement 2: 1 < |a - b|
It's possible that a-b = 2, implying that b-a = -2.
Plugging a-b=2 and b-a=-2 into 1/(a-b) < b-a, we get:
1/2 < -2?
NO.

It's possible that a-b = -2, implying that b-a = 2.
Plugging a-b=-2 and b-a=2 into 1/(a-b) < b-a, we get:
1/-2 < 2?
YES.

Since in the first case the answer is NO but in the second case the answer is YES, INSUFFICIENT.

“Is 1/(a - b) > b - a ? (1) a < b (2) 1 < |a - b|”- is a topic of the GMAT Quantitative reasoning section of GMAT. GMAT Quant section consists of a total of 31 questions. GMAT Data Sufficiency questions consist of a problem statement followed by two factual statements. GMAT data sufficiency comprises 15 questions which are two-fifths of the total 31 GMAT quant questions.

 

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