If a and b Are Integers, And |a| > |b|, is a * |b| < a

byCollegedunia Team

Question: If a and b are integers, and |a| > |b|, is a · |b| < a – b?

(1) a < 0
(2) ab >= 0

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

Correct Answer: E

Solution and Explanation:
Approach Solution 1:
Given:

a & b are both integers
|a|>|b|

Find Out:

Is a*|b|<a-b?

1) a < 0 meaning a is negative. But b could be anything as long as its absolute value is elss than a.

Let's say a=-3
B coudl equal -2, 0, or 2.
-3*|-2|<-3-(-2)?
-6<-1? .......YES
-3*|0|<-3-0
0<-3?..........NO
-3*|2|<-3-2
-6<-5...........YES
-->Not Sufficient
2) ab>=0 which means a b be either have the same sign, or one of them is 0. We know that a cannot be 0 because |a|>|b|. Therefore only b can be 0.
-3*|-2|<-3-(-2).... YES
3*|0|<-3-0...........NO
-3*|0|<-3-0............NO
3*|2|<3-2..............NO
-->INSUFFICIENT
(1&2) Combined, if a is negative, and ab>=0, this means that b is either 0 or also negative.
3*|-2|<-3-(-2).... YES
-3*|0|<-3-0............NO
--->Not Sufficient

Approach Solution 2:
Given:
a & b are both integers
|a|>|b|
Find Out:|
Is a*|b|<a-b?
Considering the first option
(1) a<0
If a=−3 and b=0, then
a∗|b|=0>a−b=−3 and the answer is NO but if a=−3 and b=−1, then
a∗|b|=−3<a−b=−2 and the answer is YES. Two different answers. Not sufficient.
Considering the second option
(2) ab≥0
Above example works here as well:
a=−3 and b=0
--> a∗|b|=0>a−b=−3
--> answer NO;
a=−3 and b=−1 →
-->a∗|b|=−3<a−b=−2
--> answer YES.
Two different answers. Not sufficient.
(1)+(2) Again the same example satisfies the stem and both statements and gives two different answers to the question whether
a∗|b|<a−b
a∗|b|<a−b.

Approach Solution 3:
(1) a<0 --> a|b|<0 (a negative |b| positive) and we already determined that when a<0 a-b<0 --> so both are negative but we can not determine is a · |b| < a – b or not.
Not Sufficient

(2) ab >= 0
a>0 b=>0 (a can not be zero as |a|>|b|) or
a<0, b<=0

a>0 b=>0 --> a|b|>0 and a – b>0 --> both are positive but we can not determine is a · |b| < a – b or not.
a<0, b<=0 --> a|b|<0 and a-b<0 --> both are negative but we can not determine is a · |b| < a – b or not.
Not Sufficient

(1)+(2) --> a<0, b<0 same thing --> a|b|<0 and a-b<0 we can not determine is a · |b| < a – b or not.

“If a and b are integers, and |a| > |b|, is a · |b| < a – b?”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book "The Official Guide for GMAT Review". 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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If a and b Are Integers, And |a| > |b|, is a * |b| < a – b? GMAT Data Sufficiency

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