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
