When integer n is divided by 15, the remainder is 5

Vincen wrote:When integer n is divided by 15, the remainder is 5. Which of the following has a remainder of 10 when divided by 15 ?

I. 3n
II. 5n
III. 4n + 10

A. I Only
B. II Only
C. III Only
D. I & II Only
E. I, II & III

Many integer properties questions can be solved by testing values

When it comes to remainders, we have a nice rule that says:
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.

When integer n is divided by 15, the remainder is 5.
So, some possible values of n are: 5, 20, 35, 50, 65, ....

Which of the following has a remainder of 10 when divided by 15 ?
Let's test a possible value of n.

Try n = 5
I. 3n = 3(5) = 15. When we divide 15 by 15, we get remainder 0. So, statement I does NOT satisfy the requirement.
ELIMINATE answer choices A, D and E

II. 5n = 5(5) = 25. When we divide 25 by 15, we get remainder 10. So, statement II DOES satisfy the requirement.

III. 4n + 10 = 4(5) + 10 = 30. When we divide 30 by 15, we get remainder 0. So, statement III does NOT satisfy the requirement.
ELIMINATE answer choice C

Answer: B

Cheers,
Brent