What is the remainder when the positive integer n is divided by 6?

Question

(1) n when divided by 12 leaves a remainder of 1
(2) n when divided by 3 leaves a remainder of 1

exc4libur · Answer

(1) n/12 = 12q + 1/12: so n could be {1,13,25,37...} and the numbers in this set divided by 6 all give a remainder of 1. sufficient.
(2) n/3 = 3q + 1/3: so n could be {1,4,7,10,13...} and the numbers in this set divided by 6 give a remainder of 1 or 4. not suf.
(A) is the answer.

BrentGMATPrepNow · Answer

Target question :    What is the remainder when the positive integer n is divided by 6?

Statement 1 : n when divided by 12 leaves a remainder of 1 
USEFUL RULE #1: "  If N divided by D equals Q with remainder R, then N = DQ + R  "
For example, since 17 divided by 5 equals 3 with remainder 2, then we can write 17 = (5)(3) + 2
Likewise, since 53 divided by 10 equals 5 with remainder 3, then we can write 53 = (10)(5) + 3

No onto the question........... 
Statement 1 does not tell us the quotient, so let's just say that n divided by 12 equals k with remainder 1
So, we can write: n = 12k + 1, where k is some integer
We can also write 12k a different way: n = (6)(2)(k) + 1 
Or n = ( 6 )(2k) + 1
As you can see, ( 6 )(2k) is a multiple of  6 , which means  ( 6 )(2k) + 1 is ONE MORE than a multiple of  6  
So, when ( 6 )(2k) + 1 (aka n) is divided by 6,  the remainder must be 1 
Since we can answer the  target question  with certainty, statement 1 is SUFFICIENT

Statement 2 : n when divided by 3 leaves a remainder of 1 
USEFUL RULE #2:   If N divided by D leaves remainder R, then the possible values of N are R, R+D, R+2D, R+3D,. . . etc.    
For example, if k divided by 5 leaves a remainder of 1, then the possible values of k are: 1, 1+5, 1+(2)(5), 1+(3)(5), 1+(4)(5), . . . etc.

So, for statement 2, some possible values of n are: 1, 4, 7, 10, 13, 16, 19, 22, etc.
Let's TEST some values...
 Case a : If n = 1, then  the remainder is 1, when n is divided by 6 
 Case b : If n = 4, then  the remainder is 4, when n is divided by 6 
Since we cannot answer the  target question  with certainty, statement 2 is NOT SUFFICIENT

Answer: A

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Salsanousi · Answer

From 1) we know  \frac{n}{12} = x + \frac{1}{12}  so adjusting it to become  n = 12x + 1  if we let  x = 0  then n = 1 , plug in in the question stem  \frac{1}{6}  remainder is 1, if we let  x = 1 , then  n = 13 , plug in  \frac{13}{6} = 2 \frac{1}{6}  another remainder of 1 and so it goes. A is sufficient.

From 2)  \frac{n}{3} = x + \frac{1}{3}  so adjusting it to become  n = 3x + 1  if we let  x = 0  then  n = 1 , plug in in the question stem  \frac{1}{6}  remainder is 1, if we let  x = 1 , then  n = 4 , plug in question stem  \frac{4}{6}  a remainder of 4. Because we get two different answers it is insufficient.

The answer is A

CrackverbalGMAT · Answer

From statement I alone, the remainder is 1 when the positive integer is divided by 12.

Therefore, n = 12k + 1, using the basic division algorithm
All multiples of 12 are necessarily divisible by 6 also. Therefore, when n is divided by 6, the remainder will be 1 since 12k is divisible by 6.

Statement I alone is sufficient to answer the question. Answer options B, C and E can be eliminated. Possible answer options are A or D.

From statement II alone, the remainder is 1 when the positive integer is divided by 3.

Therefore, n = 3k + 1.
If k = even, 3k will be a multiple of 6 and so the remainder will be 1.
If k = odd, 3k will be an odd multiple of 3 and the remainder will therefore increase by 3 i.e. the remainder will be 4.

Statement II alone is not sufficient to answer the question. Answer option D can be eliminated.

The correct answer option is A.

Hope that helps!
Aravind B T

IanStewart · Answer

Every multiple of 12 is a multiple of 6. So if, from Statement 1, n is 1 greater than a multiple of 12, then n must be 1 greater than a multiple of 6, and the remainder is 1 when we divide n by 6. So Statement 1 is sufficient.

Statement 2 is not sufficient alone, since n can equal 1 or 4, and those give remainders of 1 and 4 respectively when we divide them by 6.

What is the remainder when the positive integer n is divided by 6?

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GMAT Data Sufficiency (DS) Questions

What is the remainder when the positive integer n is divided by 6?

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