satishchandra wrote:What is the value of the integer n?
(1) n(n + 2) = 15
(2) (n + 2)^n = 125

OA is C

Target question: What is the value of the integer n?

Statement 1: n(n + 2) = 15
Expand: n^2 + 2n = 15
Set equal to zero: n^2 + 2n - 15 = 0
Factor: (n+5)(n-3) = 0
So, n = -5 or 3

Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: (n + 2)^n = 125
Well, the question tells us that n is an integer. So, this certainly limits our options.
First recognize that 125 = (5)(5)(5)
Also recognize that if n is an integer, then n+2 must be an integer.

Consider this related question. If n and x are both integers, what are some possible solutions to x^n = 125?
I can see only two case:
case a: 125^1, that is x=125 and n=1
case b: 5^3, that is x=5 and n=3

Case a doesn't work for the given equation: (n + 2)^n = 125
If n=1, then we get (1 + 2)^1 = 3

Case b does work for the given equation: (n + 2)^n = 125
If n=3, then we get (3 + 2)^2 = 125

So, statement 2 suggests that n must equal 3
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer = B

UNLESS I'M TOTALLY MISSING SOMETHING

Cheers,
Brent