Is n/12 an integer?

Question

Is n/12 an integer?

(1) n^2/144 is an integer.
(2) n/6 is an integer.

Luckisnoexcuse · Answer

(1) n could be 12 or any multiple of 12 in all cases n/12 will be an integer
Sufficient

(2) n/6 is an integer then 2n/12 will also be integer

2 * n/12 is an integer 
n/12 can be 1/2

Not sufficient

A

chetan2u · Answer

Hi,

always be careful when ever a variable is given..

(1)  \frac{n^2}{144}  is an integer.
 EASY to falter.. 
if n = 12...ans is YES
say n= \sqrt{288} , so 288/144 is an integer..
but  n/12=\sqrt{288}/12=12\sqrt{2}/12=\sqrt{2} ... ans NO
Insuff

(2)  \frac{n}{6}  is an integer.
 n=6...ans NO
n=12...ans YES 
insuff

combined..
 statement II tells u that n=6k, where k is an integer... so n is an INTEGER..
statement I now tells us that  \frac{n^2}{144}  is an integer. so if n is an integer, n has to be a multiple of 12
 ans YES
suff

GMATWhizTeam · Answer

Step 1: Analyse Question Stem

The question to be answered is,
Is  \frac{n}{12}  = integer?

In other words, 
Is n = 12 * integer.
Therefore, we are trying to find if n is a multiple of 12.

Step 2: Analyse Statements Independently (And eliminate options) – AD / BCE

Statement 1:  \frac{ n^2}{144}  is an integer.

Following the same approach as in the analysis of the question, 
 n^2  = 144 * integer.

Note that we have no information about what type of a number n is. If we knew that n was an integer, we could have concluded that the integer on the right should also be a perfect square since  n^2  would be a perfect square. However, we cannot do that here.

If integer = 1,  n^2  = 144 * 1 = 144; this means n = 12. Is n a multiple of 12? YES

If integer = 2,  n^2  = 144 * 2 = 288; this means n = 12 * root 2; Is n a multiple of 12? NO, since multiples of 12 are always numbers obtained by multiplying 12 by an integer.

The data in statement 1 is insufficient to answer the question with a definite YES or NO
Statement 1 alone is insufficient. Answer options A and D can be eliminated.

Statement 2:   \frac{n}{6 } is an integer.

This means n = 6 * integer; in other words, n is a multiple of 6
Knowing that n is a multiple of 6 is not sufficient to find out if it is also a multiple of 12.

The data in statement 2 is insufficient to answer the question with a definite YES or NO
Statement 2 alone is insufficient. Answer option B can be eliminated.

Step 3: Analyse Statements by combining

From statement 1:  n^2  = 144 * integer. 
From statement 2: n = 6 * integer

Let n = 6 * k, where k is an integer; substituting in the first equation, we have, 
36 *  k^2  = 144 * integer

Simplifying, we have,  k^2  = 4 * integer. Note that the integer on the right side should be a perfect square since  k^2  is definitely a perfect square as it is the square of an integer k.

Therefore, k = 2 * integer and hence, n = 6 * 2 * integer OR n = 12 * integer
Is n a multiple of 12? YES.

The combination of statements is sufficient to answer the question with a definite YES
Statements 1 and 2 together are sufficient. Answer option E can be eliminated.

The correct answer option is C.

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

Is n/12 an integer?

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Data Sufficiency (DS) Questions

Is n/12 an integer?

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards