If n is not equal to 0, is |n| < 4 ?

(1) n2 > 16

(2) 1/|n| > n


Statement 1: n2>16;

What will be the number whose square is greater than 16.
Square of 4 or -4 = 16. So, required number should be greater than 4….it can be 5,-5, 5.5, -5.5 etc….
Now mode of n i.e. |n| is always 0 or greater than 0. So if n is 5 or -5, mode |n| is 5.

|n| is less than 4? No.

Statement 2: 1/|n| > n, for this..n should be –ve.
When n= -1.
1/|-1| > -1; Yes.
When n=-2.
2/|-2| > -2; Yes.
When n=-10
10/|-10| > -10. Yes.

Now let’s test… |n| < 4. Yes or No.

When n= -1.
|-1|= 1.
1<4. Yes.
When n= -10
|-10| = 10
10 <4…No.

if n > 0, then fractions between 0 and 1 would make the statement 1/|n|>n true, but fractions between -1 and 0 would not. For example, if n=-1/2, then we get -2 > -1/2, which is not true. So this one means only that 0<n<1.

You had one other reason, actually, for eliminating the -1 < n < 0 possibilities: you assumed, upon starting that line of reasoning, than n > 0. So any possibilities in which n < 0 are not valid.



I'm not positive where the "negative 1" came from in your first line. I'm guessing you may be trying to account for the fact that you're assuming n is a negative? You don't have to (and shouldn't) add any negatives to the problem in order to assume that. The negatives are already included with the variable n, if we define the variable n to be negative. So you would have: 1/n > n (for n = negative) which equals 1 < n^2 = 1-n^2 < 0.

You might have tested your reasoning on this one by asking yourself: can I think of a negative number that would make this statement true?

n=-2
1/(-2) > -2
-1/2 > -2
is that true? Yes, it is. So, a negative number could work here... hmm, my reasoning that n can't be negative must be wrong. And, in fact, you had decided earlier, when you tried n>0, that n could be negative - you said that it could be between -1 and 0. That might have helped you to realize something went wrong somewhere (even though that reasoning in the first part was actually wrong as well).

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Stacey Koprince
Instructor
Director of Online Community
ManhattanGMAT

Dears,

What is the Ans:

The answer is A.

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Jamie Nelson
ManhattanGMAT Instructor