1. n^2 > 16 tells us that n is either smaller than -4 or greater than 4, since 16 = 4^2 = (-4)^2. Knowing this, we can safely say that |n| > 4, so the answer to the question in the stem will be a clear NO. 1 is therefore sufficient.

2. 1/|n| > n immediately makes me think of negative numbers. Since 4 is your "flag" here, pick two numbers on each side of -4:
a. n = -6, then 1/|n| = 1/6. In this case, |n| = 6 > 4.
b. n = -2, then 1/|n| = 1/2. However, this time you get |n| = 2 < 4.
Since there are two possible outcomes, we'll note that 2 is insufficient.

The answer will therefore be A.

DanaJ wrote:1. n^2 > 16 tells us that n is either smaller than -4 or greater than 4, since 16 = 4^2 = (-4)^2. Knowing this, we can safely say that |n| > 4, so the answer to the question in the stem will be a clear NO. 1 is therefore sufficient.

2. 1/|n| > n immediately makes me think of negative numbers. Since 4 is your "flag" here, pick two numbers on each side of -4:
a. n = -6, then 1/|n| = 1/6. In this case, |n| = 6 > 4.
b. n = -2, then 1/|n| = 1/2. However, this time you get |n| = 2 < 4.
Since there are two possible outcomes, we'll note that 2 is insufficient.

The answer will therefore be A.

Hey Dana, thanks..this approach works..
I don't know what i was up to, but it seemed to me that two statements are contradicting each other
Statement 1: n^2>16 that means n>4 or n<-4(excluding), right?
Statement 2: 1/|n|>n
i.e. n*|n|<1, now if n is negative, this inequality becomes n*(-n)<1 or n^2>-1, which is true for any negative value of n..

and if n is positive, n^2<1, that means n is b/w 1 and -1 (excluding)

now if we see statement 1 and 2, n has different set of values altogether. I am sure i am missing something here, but what??

Moreover, i usually solve modulus questions by this approach only. But lately, i am getting more incorrect than correct . So is it a better idea to plug-in values rather than scratching head by using terms (as in n or x) giving in the question?
Help!!

The two statements are NOT CONTRADICTORY as long as there is some sort of overlap in the two intervals. And you can clearly see that there is:
- statement 1: n < -4
- statement 2: n is negative

Basically, the overlap of these two statements is an infinite interval, i.e. every number that's smaller than -4.

Plugging in numbers is not a favorite strategy of mine. I usually use it for counterexamples only (i.e. when I'm trying to prove that something is false), which was the case here. It's not a full-proof strategy otherwise and picking the wrong numbers might get you in trouble. My advice: use it wisely!