chetan2u wrote:

Is \(a<-1\)?

(1) \(|a|>a+1\)

(2) \(a^2>1\)

Self made : tricky

(1) |a| - a > 1

Now if a is positive or 0, then |a| = a, so the above becomes a-a > 1 or 0 > 1, which is NOT possible. So a cannot be positive or 0.

If a is negative, |a| = -a, so the above becomes -a-a > 1 or a < -1/2. So we know that a is < -1/2, but we dont know whether a is < -1 or not (because a also might lie between -1/2 and -1). So Insufficient.

(2) a^2 > 1

This means a > 1 if a is positive, and a < -1 if a is negative. But we dont know whether a is positive or negative. So Insufficient.

Combining the two statements, first statement rules out that a can be positive or zero. So a can only be negative, and so according to statement 2, it must be < -1. Sufficient.

Hence

C answer