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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 ?

by gmattesttaker2 » Sun May 11, 2014 10:34 pm
Hello,

Can you please tell me how to solve for Statement 2 here:

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

(1) n^2 > 16

(2) 1/|n| > n


OA: A


Is |n| < 4?
=> Is + or - n < 4?
=> Is +n < 4 or -n < 4
=> Is n < 4 or n > -4?

1) n^2 > 16
=> sq. root (n^2) > sq. root ( 16 )
=> +n or -n > 4
=> n > 4 or -n > 4
=> n > 4 or n < -4

Suff.


2) 1/|n| > n

The explanation asks us to multiply |n| on both sides i.e.

1 > n |n|

and then plug in a negative value say -2

=> 1 > -2 |-2|
=> 1 > -2 x 2
=> 1 > -4

However, I am not very clear as to how this is in-sufficient. Can you please help?


Thanks a lot,
Sri
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Source: — Data Sufficiency |

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by [email protected] » Sun May 11, 2014 11:11 pm
Hi Sri,

While doing algebra helped you to deal with Fact 1, you might find that TESTing VALUES makes it easier to deal with Fact 2.

We're told N cannot = 0. We're asked is |N| < 4? This is a YES/NO question.

Fact 2: 1/|N| > N

If N = -1, 1/|-1| > -1 and the answer to the question is YES.
If N = -5, 1/|-5| > -5 and the answer to the question is NO.
Fact 2 is INSUFFICIENT.

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by GMATGuruNY » Mon May 12, 2014 3:05 am
Statement 2: 1/|n| > n

To solve, use the CRITICAL POINT approach.
Critical points occur where:
1. An expression is UNDEFINED.
2. The two sides of the inequality are EQUAL.

Here:
The expression is undefined when n=0.
1/|n| = n when n=1.

To determine where 1/|n| > n, test ONE VALUE TO THE LEFT and ONE VALUE TO THE RIGHT of each critical point.

n<0:
Plugging n=-1 into 1/|n| > n, we get:
1/|-1| > -1
1 > -1.
This works.
Thus, n<0 is a valid range.

0<n<1:
Plugging n=1/2 into 1/|n| > n, we get:
1/|1/2| > 1/2
2 > 1/2.
This works.
Thus, 0<n<1 is a valid range.

n>1:
Plugging n=2 into 1/|n| > n, we get:
1/|2| > 2
1/2 > 2.
Doesn't work.
Thus, n>1 is not a valid range.

Result:
1/|n| > n when n<0 or 0<n<1.
In other words:
n can be ANY NEGATIVE VALUE or a POSITiVE FRACTION.
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by GMATinsight » Mon May 12, 2014 7:26 am
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by hazelnut01 » Wed Mar 29, 2017 12:43 am
[email protected] wrote:Hi Sri,

While doing algebra helped you to deal with Fact 1, you might find that TESTing VALUES makes it easier to deal with Fact 2.

We're told N cannot = 0. We're asked is |N| < 4? This is a YES/NO question.

Fact 2: 1/|N| > N

If N = -1, 1/|-1| > -1 and the answer to the question is YES.
If N = -5, 1/|-5| > -5 and the answer to the question is NO.
Fact 2 is INSUFFICIENT.

GMAT assassins aren't born, they're made,
Rich
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