Data Sufficiency

Stacey Koprince wrote:Received a PM asking me to respond. From the top:

Question stem:
n is not zero, so either pos or neg. could be non-integer.
yes/no question
In order for abs. value of n to be < 4, n would have to be between -4 and 4. So I can rephrase:
is -4 < n < 4? (and n is not zero)

(1)
I'll assume "n2" means n^2. Please correct me if that's wrong.
n^2 > 16
n > +4 and n < -4
definitive no. Sufficient. Eliminate B, C, E.

(2)
1/|n| > n
You're testing this as though you have to flip the sign when you multiply things by n, but you don't. n is inside an absolute value sign, and you are multiplying by everything (including the absolute value sign), which means that it's definitely positive (or it could be zero in a different problem, but not in this one, since n does not equal zero).

So you can just say 1 > n * |n| because what you're multiplying by is definitely a positive value. Don't do what a lot of you did next, though, and rewrite this as 1 > n^2. That's not equivalent!

Try some numbers above to understand what that inequality means. If n = -2, then n * |n| = -4. -4 < 1, so this fulfills statement 2. We're allowed to choose n = -2. In this case, n is between -4 and 4, so if n = -2, then the answer to the question is yes.

Now try something else and specifically see whether you can get a "no" answer (since you already have a yes). This requires us to pick something either smaller than -4 or larger than 4. What about n = -10? Then n * |n| = -100 and -100 < 1, so this also fulfills statement 2 and we're allowed to choose n = -10. This time, the answer to the question is no.

Essentially, if we use any negative number at all for n, we'll make the statement true (because if you multiply n by the absolute value of n, you will multiple one negative and one positive number; the result of that is always negative). But some negative numbers will give us a "yes" answer and some will give us a "no" answer.

Insufficient. Answer is A.

(Notice also that the statements do not contradict, as some said above. Statements should never contradict each other.)