chetan2u wrote:

Is a < 0, if a and b are integers?

(1) \(2a^2-8b^2>0\)

(2) \(a<2b\)

(1) 2a^2 - 8b^2 > 0 . Dividing both sides by 2, we get a^2 - 4b^2 > 0 OR (a)^2 - (2b)^2 > 0 OR (a+2b)(a-2b) > 0

This doesnt tell us anything about whether a is positive or negative, so insufficient.

(2) a < 2b Or a-2b < 0. Insufficient on its own.

Combining the two statements, a-2b < 0 But (a+2b)(a-2b) > 0. This is possible only when a+2b is also < 0.

So we have both a-2b<0 and a+2b<0 OR we have a < 2b as well as a < -2b. Whether b is positive or negative, 2b and -2b will have opposite signs. a is less than both so a must be negative. And if b=0, both 2b=-2b=0, thus a<0. So in any case a will be negative only. Sufficient.

Hence

C answer