iamseer wrote:If a and b are integers, and |a| > |b|, is a · |b| < (a - b)?
(1) a < 0
(2) ab >= 0
Source: MGMAT CAT
OA : E
What is the best way to tackle such questions? Is there some technique to handle these kind of absolute value questions better?
Thanks.
The best way to solve these kind of question is squaring both sides .
Lets look at the question .
We have |a| > |b| --- squaring both sides
a^2 > b ^2 ----> a^2 - b^2 > 0 .
Now we need to know is a · |b| < (a - b)?
Thats a yes / no question . Again square both sides
a^2 b^2 < a^2 - 2ab - b^2
a^2 b^2+ 2ab < a^2 - b^2
so the question becomes is ab(ab+2) < a^2 - b^2 ?
(1) a < 0
Nothing is said about ' b' so insufficient .
(2) ab >= 0
Now if ab = 0 we get
a^2 - b^2 > 0 that is same as what is given in question so nothing new .
But if we do consider ab > 0 . We will get an answer .
So again we can not say for sure .
Insufficient .
Lets combine 1 and 2 .
we know a = negative so b is also negative as ab >0 from 2 .
But it dose not matter if a and b are positive or negative it will lead to the same situation as in statement 2 . Where ab could be equal to zero .
hence this too is not sufficient .
Ans E.
