n is not equak to 0

Question

If n is not equal to 0, is |n| < 4 ? (1) n2 > 16 (2) 1/|n| > n OAA

Brent@GMATPrepNow · Answer

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

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

GMATinsight · Answer

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

j_shreyans · Answer

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

j_shreyans · Answer

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

Brent@GMATPrepNow · Answer

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.

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

Rich.C@EMPOWERgmat.com · Answer

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).

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

Contact Rich at [email protected]

Matt@VeritasPrep · Answer

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.

Choose how you want to prepare

Get Ready for GMAT Test Day Faster with Live Online Classes

Target Test Prep EA OnDemand

Target Test Prep GMAT OnDemand

n is not equak to 0

GMAT/MBA Expert

GMAT/MBA Expert

GMAT/MBA Expert

Chicago Booth

GMAT Course Reviews

Admissions Consulting Reviews

FREE GMAT PREP RESOURCES

GMAT PREP DEAL TRACKER