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

[tuli.ashish]

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

(1) n2 > 16

(2) 1/|n| > n

In this question, while evaluating 2nd option, I made two cases of |n|

+ve case -
1/n > n , which means n2 < 1. This further means that -1 < n < 1. This value of n lies withing the range of -4 of 4

-ve Case
1/-n > n
-1/n > n
implies, n2 < -1, which is not possible, hence discard this

Hence, as only +ve of n is valid, this option is SUFFICIENT to answer the question in stem.

However, the OA says that statement 2 is Insufficient.

With regards to the official answer, how can you move |n| to the other side of Inequality when you don't know what is the sign of n?

[tuli.ashish]

No takers!!??

Can an instructer pls clarify this?

[cyapt81]

When 1/|n| is greater than n, our options for n are limited to negative numbers and fractions.

N could be any negative integer until infinity but 1/|n| would still be larger (i.e. if n is -2 1/|-2| = 1/2). |-2| is not greater than 4. However, since n could also be-5 (i.e. if n is -5 1/|-5| = 1/5) |-5| would be greater than 4 so insufficient.

N could also be any Fraction, negative or positive. If N= 1/2 then 1/|n| is greater than n (i.e. 1/.5 = 2) but n is less than 4. However if N= 1/5 then 1/|n| would still be greater than n (i.e. 1/.2 = 5) but MORE than 4.

Hence statement 2 is insufficient.

[esledge]

cyapt81 got it right--thanks! Just a small typo I'll correct for clarity.

N could also be any Fraction, negative or positive. If N= 1/2 then 1/|n| is greater than n (i.e. 1/.5 = 2) but n is less than 4. However if N= 1/5 then 1/|n| would still be greater than n (i.e. 1/.2 = 5) but MORE than 4.

That should conclude "If n is any positive or negative fraction (i.e. 0<|n|<1), then 1/|n| is always greater than n, satisfying the constraint. For all such fractions, |n| is LESS than 4."

Since there are also cases when 1/|n| > n such that |n| is MORE than 4 (i.e. all n < -4), the statement is insufficient.

[esledge]

tuli.ashish, you went wrong with your algebraic solution with a simple "flip the sign" error.

-ve Case
1/-n > n
-1/n > n
implies, n2 < -1, which is not possible, hence discard this

When you multiplied by n, you were multiplying by a number you had declared to be negative (this is your n = negative case).

Thus, -1/n > n actually implies -1 < n^2 (flipped the sign of the inequality). Since any squared number is positive and therefore greater than -1, this implies that all negative n values work as solutions.

[selvakumar.jeyakumar]

The OA to the question is not B it is A....

[Ben Ku]

The OA to the question is not B it is A....

Actually the answer IS A. (This question is titled "Absolutely Less Than 4" in the MGMAT CAT exam)