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# If n is not equal to 0, is |n| < 4 ? (1) n^2 > 16 (2)

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Manager
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Joined: 29 Jun 2009
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If n is not equal to 0, is |n| < 4 ? (1) n^2 > 16 (2) [#permalink]

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Updated on: 13 Oct 2009, 09:17
1
6
00:00

Difficulty:

45% (medium)

Question Stats:

69% (01:06) correct 31% (01:12) wrong based on 136 sessions

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

(1) n^2 > 16

(2) 1/|n| > n

Originally posted by hogann on 13 Oct 2009, 06:43.
Last edited by hogann on 13 Oct 2009, 09:17, edited 1 time in total.
Manager
Joined: 12 Oct 2009
Posts: 101
Re: If n is not equal to 0, is |n| < 4 ? (1) n^2 > 16 (2) [#permalink]

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13 Oct 2009, 07:17
1
hogann wrote:
If n is not equal to 0, is |n| < 4 ?

(1) n2 > 16

(2) 1/|n| > n

1. Given "n2 > 16" so n is greater than 4 or less than -4 so asnwer for question is |n| < 4 ? is no.
A is sufficient

2. lets assume n as -5 then 1/ |-5| = 1/5 > -5 and |-5| = 5 is not less than 4
and if we consider n as -3 then 1/|-3| = 1/3 > -3 and |-3| = 3 is less than 4
hence B is insuff

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

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13 Oct 2009, 11:14
agree with AsterMatrix
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Manager
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Re: If n is not equal to 0, is |n| < 4 ? (1) n^2 > 16 (2) [#permalink]

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13 Oct 2009, 11:54
2
[quote="asterixmatrix
1. Given "n2 > 16" so n is greater than 4 or less than -4 so asnwer for question is |n| < 4 ? is no.
A is sufficient

2. lets assume n as -5 then 1/ |-5| = 1/5 > -5 and |-5| = 5 is not less than 4
and if we consider n as -3 then 1/|-3| = 1/3 > -3 and |-3| = 3 is less than 4
hence B is insuff

[/quote]

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

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01 Jan 2014, 13:25
hogann wrote:
If n is not equal to 0, is |n| < 4 ?

(1) n^2 > 16

(2) 1/|n| > n

Edit to fix exponent

What's the range for the second statement? Is it x<1?

Let us know

Cheers!
J
Math Expert
Joined: 02 Sep 2009
Posts: 46284
Re: If n is not equal to 0, is |n| < 4 ? (1) n^2 > 16 (2) [#permalink]

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02 Jan 2014, 05:33
3
1
jlgdr wrote:
hogann wrote:
If n is not equal to 0, is |n| < 4 ?

(1) n^2 > 16

(2) 1/|n| > n

Edit to fix exponent

What's the range for the second statement? Is it x<1?

Let us know

Cheers!
J

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

Question basically asks is -4<n<4 true.

(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, hence we can not answer the question. Not sufficient.

As you can see we don't really want the complete range for (2) to see that this statement is not sufficient, but still if interested:

1/|n| > n --> n*|n| < 1.

If n<0, then we'll have -n^2<1 --> n^2>-1. Which is true. So, n*|n| < 1 holds true for any negative value of n.
If n>0, then we'll have n^2<1 --> -1<n<1. So, n*|n| < 1 also holds true for 0<n<1.

Thus 1/|n| > n holds true if n<0 and 0<n<1.

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

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16 Feb 2018, 19:03
Hi All,

This question is based around a couple of different patterns (some obvious, some not). You can TEST VALUES to answer the question...

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

Fact 1: N^2 > 16

You probably recognize that this means that N > 4 or N < -4. This Fact gives us a consistent result; here's the proof:

IF...
N = 5, then the answer to the question is NO.

IF....
N = -5, then the answer to the question is NO.

No matter what value you use for N, under these 'restrictions', the answer to the question is ALWAYS NO.
Fact 1 is SUFFICIENT

Fact 2: 1/|N| > N

You can approach this Fact in a couple of different ways: with Algebra and Number Properties or by TESTing VALUES. Notice how the 'left side' of the inequality will ALWAYS be POSITIVE.....

IF...
N = -2, then 1/|-2| is > -2 and the answer to the question is YES.

IF...
N = -5, then 1/|-5| is > -5 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 ? (1) n^2 > 16 (2)   [#permalink] 16 Feb 2018, 19:03
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