What is the remainder when the positive integer N is divided by 12?

Question

(1) When N is divided by 6, the remainder is 4
(2) When N is divided by 3, the remainder is 1

Source: 4Gmat

mikemcgarry · Answer

Dear alphonsa , Something is fishy about this problem. Are you sure you have the correct OA listed? If N = 16, then When N is divided by 6, the remainder is 4 When N is divided by 3, the remainder is 1 When N is divided by 12, the remainder is also 4. If N = 22, then When N is divided by 6, the remainder is 4 When N is divided by 3, the remainder is 1 When N is divided by 12, the remainder is 10. Thus, two different numbers can satisfy both statements but given different answers to the prompt question. That means the answer should be (E) . Is there more information in the problem? Something doesn't work here. Mike :-)

alphonsa · Answer

Hi Mike... Thanks. Well, the answer mentioned was C ..

Shall I change it to E? I cross-checked with the material again.

mikemcgarry · Answer

Hmmm. Are you sure that every last detail was copied correctly? I know nothing about this source, but if the very first question I see from it has an incorrect answer, that's hardly a vote of confidence. Perhaps leave it with no OA, because flawed questions are not going to help anyone's practice. Mike :-)

BrushMyQuant · Answer

I wrote a detailed post on  How to Solve Remainder Problems . Try going through it to get more clarity on the topic.
 
STAT1: N=6K + 4
N can be 10, 16,...
If N is 10 then N/12 remainder will be 10
If N is 16 then N/12 remainder will be 4
So, NOT SUFFICIENT

STAT2: N=3T + 1
N can be 10, 16,...
If N is 10 then N/12 remainder will be 10
If N is 16 then N/12 remainder will be 4
So, NOT SUFFICIENT

Taking both together also we have these two cases
N can be 10, 16,...
If N is 10 then N/12 remainder will be 10
If N is 16 then N/12 remainder will be 4

So, we dont have a definite value for remainder in any case so answer will be E
Hope it helps!

Bunuel  Please update OA to E. Thank you

Bunuel · Answer

_______________________
Done. Thank you.

Kinshook · Answer

Asked: What is the remainder when the positive integer N is divided by 12?

(1) When N is divided by 6, the remainder is 4
Remainder when the positive integer N is divided by 12 = {4,10}
NOT SUFFICIENT

(2) When N is divided by 3, the remainder is 1
Remainder when the positive integer N is divided by 12 = {1,4,7,10}
NOT SUFFICIENT

(1) + (2) 
(1) When N is divided by 6, the remainder is 4
Remainder when the positive integer N is divided by 12 = {4,10}
(2) When N is divided by 3, the remainder is 1
Remainder when the positive integer N is divided by 12 = {1,4,7,10}
Combining we get 
Remainder when the positive integer N is divided by 12 = {4,10}
NOT SUFFICIENT

IMO E

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What is the remainder when the positive integer N is divided by 12?

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