When the integer n is divided by 6, the remainder is 3, Which of the following is NOT a multiple of 6?

(A) n – 3
(B) n + 3
(C) 2n
(D) 3n
(E) 4n


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When n is split into groups of 6, 3 is left over.
If you remove 3 from n, there will be only groups of 6 leftover. So (n - 3) will be divisible by 6.
If you add 3 to n, the remaining will also form a complete group of 6 and hence there will be only groups of 6. So (n + 3) will be divisible by 6.

When you double n, 3 left over will become 6 and so we will have only groups of 6. Hence 2n will be divisible by 6.
If 2n is divisible by 6, 4n must be divisible by 6 too.

When you triple n, 3 will still be left over. So 3n will not be divisible by 6.

Answer (D)
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n=6q+3→
3n=18q+9
18q is a multiple of 6
9 is not a multiple of 6
so 18q+9 is not a multiple of 6
3n
D