mehaksal wrote:What is the value of integer j ?

1. |J| = J^-1
2. J^J=1

(1) |J| = J^-1 implies |J| = 1/J
Now |J| will always be positive.
|J| = 1/J implies J² = 1. So, J = 1 or -1. But J has to be positive always. So, J = 1; SUFFICIENT.

(2) J^J = 1
If J = 0, then 0^0 = 1
If J = 1, then 1^1 = 1
No definite answer; NOT sufficient.

The correct answer is A.

The issue of the value of 0^0 has been discussed many times on this site.
Here's one such example: https://www.beatthegmat.com/zero-raised- ... 69042.html

When you check the official guide, you'll see that the test-makers don't address the issue. When they discuss powers of zero, they restrict the conversation to positive bases and say that x^0 = 1 when x>0. Of course, I'm pretty sure that they would concede that x^0 = 1 when x<0.

However, since the test-maker makes no attempt to discuss the value of 0^0, I'm quite sure that you'd never find an official GMAT question that hinges on this.

Cheers,
Brent