|N+5|=5

--> N + 5 = 5 --> N = 0

or

N + 5 = - 5 --> N = -10

THus either N = 0 or N = -10

what we need to find out is N = ?

1) N^2 is not equal to 0
--> this tells us that N is not equal to 0
thus N = -10
Sufficient

2) N^2 + 10N = 0

N(N + 10) = 0
N = 0 or N = -10

THus we still dont know what the exact value of N is

So Insufficient

Given |N+5|=5 => N = 0 or N = -10

1. N^2 != 0 => N!=0 so N =-10.
2. N^2+10N =0 => N(N+10)=0 => N = 0 or N = -10

So 1 will give the unique value of N so A is the Answer.

In order for |N+5|=5 to be true N must either be 0 or -10

(1) N^2 not equal 0, tells you that N is not 0 (since 0^2 equals 0), therefore N must be -10 => sufficient

(2) N^2 + 10N = 0 tells you that N can be either -10 or 0, which doesn't help you much in determining N, => insufficient

so the answer is: A

Panjieming,

Add a spoiler to your answers in your posts in future. That's the normal
practice here so that it won't spoil the approach to our answer...

PANJIEMING wrote:Any clue how to prove the answer, which is [A]
|N+5|=5, what is the value of N?
1) N^2 is not equal to 0
2) N^2 + 10N = 0
Thanks for the input.

I am wary of inequality and absolute values. In Q regarding Absolute values if squaring is possible then that for me is the easiest way. More so as in this problem the two hints are in form of N² and N²+10 respectively

|N+5|=5 or (N+5)² = 25 N² + 10N + 25 = 25 got rid of | |

1) N² <> 0 , N² has to be a + ve integer = 10 N or N is 1/10 of that +ve integer . Sufficient
2) if in the eq N² + 10N + 25 = 25
N² + 10N = 0 LHS = 25 = RHS . that is no linear eq so Insuff.