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

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If n is not equal to 0, is |n| < 4 ?  [#permalink]

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New post 21 Feb 2012, 20:22
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If n is not equal to 0, is |n| < 4 ?

(1) n^2 > 16
(2) 1/|n| > n

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Re: DS: Inequalities  [#permalink]

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New post 21 Feb 2012, 22:14
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1
If n is not equal to 0, is |n| < 4 ?

Question basically asks is -4<n<4?

(1) n^2>16 --> n>4 or n<-4, the answer to the question is NO. Sufficient.

(2) 1/|n| > n --> this is true for all negative values of n (complete range for 1>n*|n| is n<1), hence we can not answer the question. Not sufficient.

Answer: A.

For hard inequality and absolute value questions with detailed solutions check this: inequality-and-absolute-value-questions-from-my-collection-86939-40.html

Hope it helps.
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Re: If n is not equal to 0, is |n| < 4 ? (1) n^2 >16 (2) 1/|n|>n  [#permalink]

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New post 21 Feb 2012, 22:22
>> 1/|n| > n --> this is true for all negative values of n

Bunuel, how did you deduce that?

I converted 1/|n| > n to:
|n|*n < 1
...but then, had to try out a couple numbers less than 1 to arrive the above conculsion.
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Re: If n is not equal to 0, is |n| < 4 ? (1) n^2 >16 (2) 1/|n|>n  [#permalink]

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New post 21 Feb 2012, 22:42
1
fxsunny wrote:
>> 1/|n| > n --> this is true for all negative values of n

Bunuel, how did you deduce that?

I converted 1/|n| > n to:
|n|*n < 1
...but then, had to try out a couple numbers less than 1 to arrive the above conculsion.


Complete range for which 1/|n| > n holds true is n<1. But you should be able to get that it holds true for n<0 at the moment you realize that 1/|n| is always positive, so if n is negative we'll have 1/|n|=positive>n=negative.

Hope it's clear.
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Re: If n is not equal to 0, is |n| < 4 ?  [#permalink]

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New post 28 May 2015, 17:15
Hi All,

This DS question can be solved with a mix of Number Properties and TESTing VALUES.

We're told that N is NOT equal to 0. We're asked if |N| < 4. This is a YES/NO question.

Fact 1: N^2 > 16

Since we're dealing with a squared term, we have to consider both positive and negative possibilities.

N^2 > 16 means that....
N can be greater than 4

and

N can be less than -4

So, N could be 4.1, 4.7, 5, 6, 7, etc. Each of these values would gives us a NO answer.
N could also be -4.1, -4.2, -5, -6, -8, etc. Each of these values would also gives us a NO answer.
Given the restrictions in Fact 1, the answer to the question is ALWAYS NO.
Fact 1 is SUFFICIENT

Fact 2: 1/|N| > N

Since |N| will always be positive in this question (since N CANNOT be 0), we know that ANY negative value for N will fit Fact 2...

IF....
N = -1
1/|-1| > -1
|-1| IS < 4 and the answer to the question is YES.

IF....
N = -5
1/|-5| > -5
|-5| is NOT < 4 and the answer to the question is NO.
Fact 2 is INSUFFICIENT

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Re: If n is not equal to 0, is |n| < 4 ?  [#permalink]

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New post 06 Mar 2017, 18:17
1
dvinoth86 wrote:
If n is not equal to 0, is |n| < 4 ?

(1) n^2 > 16
(2) 1/|n| > n


We need to determine whether |n| < 4.

Statement One Alone:

n^2 > 16

We can simplify the information in statement one and we have:

√n^2 > √16

|n| > 4

So, the answer to the question “Is |n| < 4?” is no. Statement one is sufficient to answer the question.

Statement Two Alone:

1/|n| > n

We can simplify the information in statement two and we have:

1 > |n| x n

Since n is not equal to 0, |n| is positive. Multiplying both sides of an inequality by a positive quantity will not affect the inequality sign.

However, we still cannot answer the question. For instance, if n = -5, then 1 > |-5| x -5 and |n| IS NOT less than 4. However, if n = -3, then 1 > |-3| x -3 and |n| IS less than 4. Statement two is not sufficient to answer the question.

Answer: A
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Re: If n is not equal to 0, is |n| < 4 ?  [#permalink]

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Re: If n is not equal to 0, is |n| < 4 ? &nbs [#permalink] 26 Jul 2018, 09:21
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