The problem statement tells us that the absolute value of n+5=5. Thus, we have either that:
a) n+5=5, and n=0 or
b)n+5 = -5, and n=-10
From statement 1, we are told n^2 is not equal to 0. Thus, n is not equal to 0. So, n must be -10. Statement 1 gives us sufficient information to solve for n.
From statement 2, we are told:
n^2 + 10n = 0. We can rewrite this:
n(n+10)=0.
This equation has two solutions: n=0 and n=-10. Thus, statement 2 does not give us a definitive answer for n and is not sufficient.
Since only statement 1 was sufficient, the answer is A.
Tatiana Becker | GMAT Instructor | Veritas Prep
