Inequality - MGMAT

gughanbose wrote:If (a^2)*b > 1 and b < 2, which of the following could be the value of a?

a²b > 1 ---> a² and b are of same sign
As a² is always positive, b is also positive.

Hence, a² > 1/b and 1/b > 1/2
Hence, a² > 1/2

Only option D works.

The correct answer is D.

We can also work backwards from the answer choices here, to see which one works:

A. If a=1/2, then (1/4)*b has to be greater than 1, which means b has to be greater than 4. But b has to be less than 2, so this doesn't work.

B. If a=1/4, then (1/16)*b has to be greater than 1, which means b has to be greater than 16. But b has to be less than 2, so this doesn't work.

C. a^2 here would be the same as in A. Doesn't work.

D. If a=-2, then (4)*b has to be greater than 1, then b has to be greater than 1/4. b can be any number between 1/4 and 2. This works!

E. If a=2/3, then (4/9)*b has to be greater than 1, so b has to be greater than 9/4. 9/4 is greater than 2, so this doesn't work.