If the remainder is 7 when positive integer n is divided by

[uptowngirl92]

If the remainder is 7 when positive integer n is divided by 18, what is the remainder when n is divided by 6 ?

(A) 0

(B) 1

(C) 2

(D) 3

(E) 4

[ssmiles08]

IMO B.

N= 18Q1 + 7

N = 6Q2 + R

6(Q2-3*Q1) = 7-R

(7-R)/6 ---> must be an integer; so the only possible value for R can be 1.

You can also test this with numbers:

Lets say n = 25

25/18 gives the remainder of 7

25/6 gives the remainder of 1.

[tohellandback]

without calculation:

number divisible by 18 must be divisible by 6
here remainder is 7, if we add 11 it becomes divisible by 18.
now the remainder after dividing by 6 should be such that (remainder+11) must be a multiple of 6.

1 is the answer

Thanks