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Prime number division

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Prime number division

by ousek » 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 ?


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Re: Prime number division

by Pranay » 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.

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

by ousek » 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... :?
Curious...

What is your opinion ?

Another explanation ?
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by Ian Stewart » 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.
For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

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by ousek » 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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by Umar82 » 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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by sureshbala » 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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by shreeuec » Fri Mar 11, 2011 10:07 pm
Thank you Suresh thats a very good explaination
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