sarahw_gmat wrote:If a and b are integers, and |a| > |b|, is a · |b| < a - b?
(1) a < 0
(2) ab 0
OA : E
As statement 2 is incomplete, I shall only be working on statement 1.
|a| > |b| means the distance between 0 and a is greater than that of between 0 and b.
The question is : a · |b| < a - b?
To help you comprehend the solution, put a number line and specify the relative positions of a and b . -a ------ -b ----0--- b------- a [Here note that b can also be 0]
Statement 1: a<0
Now consider the left hand side of the line. And take points.
For example: a = -4, b = -2,
a · |b| < a - b
= -4. 2 < -4 -(-2)
= -8 < -2 ....Yes
But, b can be 0, check with that too.
a= -4, and b=0
a · |b| < a - b
= -4 . 0 < -4 -0
= 0 < -4 ......No
Hence statement 1 alone is insufficient.
Therefore the answer is definitely not A or D.
