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by Brent@GMATPrepNow » Wed Sep 03, 2014 3:22 am
j_shreyans wrote:If n is not equal to 0, is |n| < 4 ?

(1) n² > 16

(2) 1/|n| > n
Target question: Is |n| < 4 ? YES/NO question

Given: n is not equal to 0

Statement 1: n² > 16
This means that n > 4 or n < -4
Check each case.
case a: n > 4. If this is true, then NO, it is not the case that |n| < 4
case b: n < -4. If this is true, then NO, it is not the case that |n| < 4
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: 1/|n| > n
To simplify matters, let's multiply both sides by |n| to get: 1 > n|n|
There are several values of n that satisfy this condition. Here are two:
Case a: n = -1, in which case it IS the case that |n| < 4
Case b: n = -5, in which case it is NOT the case that |n| < 4
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Answer = A

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by GMATinsight » Wed Sep 03, 2014 3:47 am
j_shreyans wrote:If n is not equal to 0, is |n| < 4 ?

(1) n2 > 16

(2) 1/|n| > n

OAA
Question : Is |n| < 4 ?
Question : Is -4 < n < 4 ?

Statement 1) n^2 > 16
i.e. n>4 or n<-4
SUFFICIENT

Statement 2) 1/|n| > n
i.e. 1/|n| > n
i.e. 1 > |n|n
With this result we can infer that n must be less than 1 but since n can be negative number as well whole absolute value can lie with the range asked in the question but may also lie outside the range
therefore, INSUFFICIENT

Answer: Option A
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by j_shreyans » Thu Oct 02, 2014 8:18 am
Brent@GMATPrepNow wrote:
j_shreyans wrote:If n is not equal to 0, is |n| < 4 ?

(1) n² > 16

(2) 1/|n| > n
Target question: Is |n| < 4 ? YES/NO question

Given: n is not equal to 0

Statement 1: n² > 16
This means that n > 4 or n < -4
Check each case.
case a: n > 4. If this is true, then NO, it is not the case that |n| < 4
case b: n < -4. If this is true, then NO, it is not the case that |n| < 4
Since we can answer the target question with certainty, statement 1 is SUFFICIENT
Statement 2: 1/|n| > n
To simplify matters, let's multiply both sides by |n| to get: 1 > n|n|
There are several values of n that satisfy this condition. Here are two:
Case a: n = -1, in which case it IS the case that |n| < 4
Case b: n = -5, in which case it is NOT the case that |n| < 4
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT
Hi Brent ,

One thing in statement 2 - how can we multiply by|n| because we don't the sign of n .

Pls correct me if i am wrong

Answer = A

Cheers,
Brent
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by j_shreyans » Thu Oct 02, 2014 8:24 am
Brent@GMATPrepNow wrote:
j_shreyans wrote:If n is not equal to 0, is |n| < 4 ?

(1) n² > 16

(2) 1/|n| > n
Target question: Is |n| < 4 ? YES/NO question

Given: n is not equal to 0

Statement 1: n² > 16
This means that n > 4 or n < -4
Check each case.
case a: n > 4. If this is true, then NO, it is not the case that |n| < 4
case b: n < -4. If this is true, then NO, it is not the case that |n| < 4
Since we can answer the target question with certainty, statement 1 is SUFFICIENT
Statement 2: 1/|n| > n
To simplify matters, let's multiply both sides by |n| to get: 1 > n|n|
There are several values of n that satisfy this condition. Here are two:
Case a: n = -1, in which case it IS the case that |n| < 4
Case b: n = -5, in which case it is NOT the case that |n| < 4
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT
Hi Brent ,

One thing in statement 2 - how can we multiply by|n| because we don't the sign of n .

Pls correct me if i am wrong
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by Brent@GMATPrepNow » Thu Oct 02, 2014 8:29 am
Hi j_shreyans,

You are correct in that we don't know whether n is positive or negative, so we can't multiply both sides by n.
However, we are actually multiplying both sides by |n|, and this is okay because we know that |n| is POSITIVE.

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by [email protected] » Thu Oct 02, 2014 11:00 pm
Hi j_shreyans,

Fact 2 includes a great Number Property pattern that you can use to avoid any complex algebra that you might be thinking about doing. Here's why:

Fact 2: 1/|N| > N

We're told at the beginning of the prompt that N CANNOT = 0, so N is either a positive or negative number.

|N| will ALWAYS be positive, so 1/|N| will always be positive.

We're told that 1/|N| > N, so N can be ANY NEGATIVE value and the inequality will be true. This is really helpful, since the questions asks If |N| < 4?

If N = -1, then the answer to the question is YES.
If N = - 10, then the answer to the question is NO.
Fact 2 is INSUFFICIENT (and no excessive math is required to prove it).

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by Matt@VeritasPrep » Fri Oct 03, 2014 12:08 pm
j_shreyans wrote:One thing in statement 2 - how can we multiply by|n| because we don't the sign of n .

Pls correct me if i am wrong
An important note here: it's not that we CAN'T multiply by n, we just have to consider multiple cases: the case in which n is positive, and the case in which n is negative.

For instance, suppose we have m/n > 3.

If n > 0, then we have m > 3n.
If n < 0, then we have m < 3n.

Don't feel like you CAN'T do anything: you can! Just make sure to consider both options, when appropriate.
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