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

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

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New post Updated on: 13 Oct 2009, 09:17
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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.
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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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New post 13 Oct 2009, 07:17
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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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New post 13 Oct 2009, 11:14
agree with AsterMatrix
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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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New post 13 Oct 2009, 11:54
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[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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New post 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 :)
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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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New post 02 Jan 2014, 05:33
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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.

Answer: A.

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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New post 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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