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Prime number division

This topic has 1 expert reply and 6 member replies
ousek Junior | Next Rank: 30 Posts
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Prime number division

Post 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

Confused Does anyone have an idea of the answer ?


Ousek

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sureshbala Master | Next Rank: 500 Posts
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Post 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"

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shreeuec Newbie | Next Rank: 10 Posts Default Avatar
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Post Fri Mar 11, 2011 10:07 pm
Thank you Suresh thats a very good explaination

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Umar82 Junior | Next Rank: 30 Posts Default Avatar
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Post Tue May 12, 2009 2:29 pm
The answer is (E)

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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ousek Junior | Next Rank: 30 Posts
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Post 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,

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Ian Stewart GMAT Instructor
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Post 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.

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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

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ousek Junior | Next Rank: 30 Posts
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Post Tue May 12, 2009 3:27 am
The official answer is B.
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:
Arrow 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... Confused
Curious...

What is your opinion ?

Another explanation ?
Ousek

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Pranay Senior | Next Rank: 100 Posts Default Avatar
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Post 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

Confused Does anyone have an idea of the answer ?


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

Not sure between the two. Please post the answer once someone reaches the answer.

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