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
Prime number division
This topic has expert replies
I am not sure .. but have narrowed down to two options B and E.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
Not sure between the two. Please post the answer once someone reaches the answer.
- ousek
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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 ?
Ousek
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 ?
Ousek
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- Ian Stewart
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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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- ousek
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Not in mine... it does clearly ask for R(n/12), which makes no sense.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.
Nevertheless, thank for your confirmation, Ian !
Best regards,
- sureshbala
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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"
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"