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jainrahul1985
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integer
Source: Beat The GMAT — Data Sufficiency |
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neelgandham
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If a and b are integers, and |a| > |b|, is a · |b| < a - b?
|a| > |b|
All conditions satisfying the equation (Taking numbers instead of variables for easy explanation) are written below
i ) a = -1, b = 0
ii ) a = 1, b = 0
iii) a = -2, b = -1
iv ) a = 2, b = -1
v ) a = -2, b = 1
vi ) a = 2 , b = 1
(1) a < 0
These three condns. from the list above satisfy the condition a < 0
i ) a = -1, b = 0 => Is a · |b| < a - b ? => -1*0 < -1-0 ? => 0 < -1 NO is the answer
iii) a = -2, b = -1 => Is a · |b| < a - b ? => -2*-1 < -2+1 ? =>-2 < -1 YES is the answer
v ) a = -2, b = 1 => Is a · |b| < a - b ? => -2*1 < -2-1 ? =>-2 < -3 NO is the answer
We have two different answers YES and NO, Hence Insufficient
(2) ab >= 0
These four condns. from the list above satisfy the condition ab >= 0
i ) a = -1, b = 0 => Is a · |b| < a - b ? => -1*0 < -1-0 ? => 0 < -1 ? NO is the answer
ii ) a = 1, b = 0 => Is a · |b| < a - b ? => 1*0 < 1-0 ? => 0 < 1 ? YES is the answer
iii) a = -2, b = -1 => Is a · |b| < a - b ? => -2*-1 < -2+1 ? => 2 < -1 ? NO is the answer
vi ) a = 2 , b = 1 => Is a · |b| < a - b ? => 2*1 < 2-1 ? => 2 < 1 ? NO is the answer
We have two different answers YES and NO, Hence Insufficient
Joining both the condns. a < 0 and ab >=0 we get the following conditions
From condition a < 0
i ) a = -1, b = 0 => Is a · |b| < a - b ? => -1*0 < -1-0 ? => 0 < -1 NO is the answer
iii) a = -2, b = -1 => Is a · |b| < a - b ? => -2*-1 < -2+1 ? =>-2 < -1 YES is the answer
From condition ab >= 0
i ) a = -1, b = 0 => Is a · |b| < a - b ? => -1*0 < -1-0 ? => 0 < -1 ? NO is the answer
iii) a = -2, b = -1 => Is a · |b| < a - b ? => -2*-1 < -2+1 ? => 2 < -1 ? NO is the answer
We still have two different answers YES and NO, Hence Insufficient Option E
|a| > |b|
All conditions satisfying the equation (Taking numbers instead of variables for easy explanation) are written below
i ) a = -1, b = 0
ii ) a = 1, b = 0
iii) a = -2, b = -1
iv ) a = 2, b = -1
v ) a = -2, b = 1
vi ) a = 2 , b = 1
(1) a < 0
These three condns. from the list above satisfy the condition a < 0
i ) a = -1, b = 0 => Is a · |b| < a - b ? => -1*0 < -1-0 ? => 0 < -1 NO is the answer
iii) a = -2, b = -1 => Is a · |b| < a - b ? => -2*-1 < -2+1 ? =>-2 < -1 YES is the answer
v ) a = -2, b = 1 => Is a · |b| < a - b ? => -2*1 < -2-1 ? =>-2 < -3 NO is the answer
We have two different answers YES and NO, Hence Insufficient
(2) ab >= 0
These four condns. from the list above satisfy the condition ab >= 0
i ) a = -1, b = 0 => Is a · |b| < a - b ? => -1*0 < -1-0 ? => 0 < -1 ? NO is the answer
ii ) a = 1, b = 0 => Is a · |b| < a - b ? => 1*0 < 1-0 ? => 0 < 1 ? YES is the answer
iii) a = -2, b = -1 => Is a · |b| < a - b ? => -2*-1 < -2+1 ? => 2 < -1 ? NO is the answer
vi ) a = 2 , b = 1 => Is a · |b| < a - b ? => 2*1 < 2-1 ? => 2 < 1 ? NO is the answer
We have two different answers YES and NO, Hence Insufficient
Joining both the condns. a < 0 and ab >=0 we get the following conditions
From condition a < 0
i ) a = -1, b = 0 => Is a · |b| < a - b ? => -1*0 < -1-0 ? => 0 < -1 NO is the answer
iii) a = -2, b = -1 => Is a · |b| < a - b ? => -2*-1 < -2+1 ? =>-2 < -1 YES is the answer
From condition ab >= 0
i ) a = -1, b = 0 => Is a · |b| < a - b ? => -1*0 < -1-0 ? => 0 < -1 ? NO is the answer
iii) a = -2, b = -1 => Is a · |b| < a - b ? => -2*-1 < -2+1 ? => 2 < -1 ? NO is the answer
We still have two different answers YES and NO, Hence Insufficient Option E
Anil Gandham
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Anurag@Gurome
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Take the following two examples,jainrahul1985 wrote:If a and b are integers, and |a| > |b|, is a · |b| < a - b?
(1) a < 0
(2) ab >= 0
- 1. a = -2 and b = -1 --> a|b| = -2 < a - b = -1
2. a = -2 and b = -0.5 --> a|b| = -1 > a - b = -1.5
Hence, both statements together is also not sufficient to answer the question.
The correct answer is E.
Anurag Mairal, Ph.D., MBA
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