integer

[jainrahul1985]

If a and b are integers, and |a| > |b|, is a · |b| < a - b?
(1) a < 0
(2) ab >= 0
OA E

[mandarchougule]

IMO E

[neelgandham]

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

[Anurag@Gurome]

If a and b are integers, and |a| > |b|, is a · |b| < a - b?
(1) a < 0
(2) ab >= 0

Take the following two examples,

• 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

Both the examples satisfy all the given conditions but for the 1st one the answer YES and for the 2nd one the answer is NO.

Hence, both statements together is also not sufficient to answer the question.

The correct answer is E.