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

Question

(1) When 2k is divided by 12, the remainder is 2.
(2) When 3k is divided by 12, the remainder is 3.

nick1816 · Answer

Statement 1-
k=1 mod 6
Hence 
k=1 mod 12
or
k=7 mod 12

Insufficient

Statement 2-
k= 1 mod 4

Hence 
k=1 mod 12
or k=5 mod 12
or k= 9 mod 12

Insufficient

Combining both equations
k=1 mod 12
 Sufficient

TestPrepUnlimited · Answer

Statement 1:

We can divide all numbers by 2 and translate this to "when k is divided by 6, the remainder is 1". Then we can write k as  k = 6i + 1  where i is any integer. If we divide k by 12 we can get either 1 or 7 as the remainder.

Statement 2:

Using the technique above: "When k is divided by 4, the remainder is 1".  k = 4i + 1 , when we divide k by 12 we can get 1, 5, or 9 as the remainder.

Statement 3:

Combined we can only have remainders of 1, sufficient. Another neat way to see this is to subtract (1) from (2) to get "When k is divided by 12, the remainder is 1". This works since both expressions are divided by 12, an additional k divided by 12 gives an additional remainder of 1.

Ans: C

Archit3110 · Answer

#1
When 2k is divided by 12, the remainder is 2.
k=13,7 insufficient
#2
When 3k is divided by 12, the remainder is 3
k=9,17 insufficient
from 1 &2
we observe that at k=12 remainder values are 2 &3 so integer k has to be 12 hence remainder 0
IMO C sufficient

Harshjha001 · Answer

Shouldn't the answer be D ?

Statement 1 : 2k/12 gives remainder 2 . This means each k leaves a remainder 1 . 
Same is the case with statement 2 .

Bunuel

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

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