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## Prime number division

This topic has 1 expert reply and 6 member replies
ousek Junior | Next Rank: 30 Posts
Joined
07 Jul 2008
Posted:
20 messages
Target GMAT Score:
700+

#### Prime number division

Mon May 11, 2009 11:36 pm
Hi,

I got this question from the ETS paper-based of GMAT #37 :

If n is a prime number greater than 3, what is the
remainder when n is divided by 12?

(A) 0
(B) 1
(C) 2
(D) 3
(E) 5

Does anyone have an idea of the answer ?

Ousek

sureshbala Master | Next Rank: 500 Posts
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Followed by:
9 members
84
Tue May 12, 2009 6:31 pm
The question has to be this....

If n is a prime number greater than 3, what is the remainder when n^2 is divided by 12.

Any prime number greater than 3 can be expressed in the form of 6K+1 or 6k-1.

So n^2 = 36k^2 + 12k + 1 or 36k^2 -12k +1

So it is now clear that in either case the remainder when n^2 is divided by 12 is 1.

Of course you can always consider examples and finish this as the options do not contain "Cannot be determined"

shreeuec Newbie | Next Rank: 10 Posts
Joined
10 Jul 2010
Posted:
2 messages
1
Fri Mar 11, 2011 10:07 pm
Thank you Suresh thats a very good explaination

Pranay Senior | Next Rank: 100 Posts
Joined
05 May 2009
Posted:
59 messages
1
Tue May 12, 2009 1:19 am
ousek wrote:
Hi,

I got this question from the ETS paper-based of GMAT #37 :

If n is a prime number greater than 3, what is the
remainder when n is divided by 12?

(A) 0
(B) 1
(C) 2
(D) 3
(E) 5

Does anyone have an idea of the answer ?

Ousek
I am not sure .. but have narrowed down to two options B and E.

ousek Junior | Next Rank: 30 Posts
Joined
07 Jul 2008
Posted:
20 messages
Target GMAT Score:
700+
Tue May 12, 2009 3:27 am
According to me, it is not the only answer possible, as you discovered.
R(17/12)=5
R(13/12)=1

Perhaps is the question wrongly designed. Further prospection on the subject gave me the following rules:
If n is a prime number greater than 3, then the remainder of (n^2)/12 is 1.
This is the only one explanation I see. I even so asked to see if I felt in the analysis. Actually, this test sheet is marked "proofed" by GMAC...
Curious...

Another explanation ?
Ousek

### GMAT/MBA Expert

Ian Stewart GMAT Instructor
Joined
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GMAT Score:
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Tue May 12, 2009 4:15 am
In the version of the paper test that I have, it does ask for the remainder when n^2 is divided by 12, and not when n is divided by 12. If the question asks about n, of course there is more than one right answer, which never happens on the GMAT.

_________________
If you are looking for online GMAT math tutoring, or if you are interested in buying my advanced Quant books and problem sets, please contact me at ianstewartgmat at gmail.com

ousek Junior | Next Rank: 30 Posts
Joined
07 Jul 2008
Posted:
20 messages
Target GMAT Score:
700+
Tue May 12, 2009 4:24 am
Ian Stewart wrote:
In the version of the paper test that I have, it does ask for the remainder when n^2 is divided by 12, and not when n is divided by 12.
Not in mine... it does clearly ask for R(n/12), which makes no sense.

Nevertheless, thank for your confirmation, Ian !

Best regards,

Umar82 Junior | Next Rank: 30 Posts
Joined
21 Nov 2008
Posted:
21 messages
1
Tue May 12, 2009 2:29 pm

13/12 gives remainder of 1

17/12 gives remainder 5

29/12 gives remainder 5

go with the one that occur the most in my opinion, however the wording of this questions seems wrong

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