n/ 20 = q + 15

n = 20q + 15

n = 5( 4q + 3)

Therefore, n must be divisible by 5.

The best answer is B.

n= 20*q+ 15
= 5( 4q+3)

must be a divisor of 5 IMO B

let Q = quotient

n = 20*Q + 15
try different values of Q
n = 20(1) + 15 = 35
n = 20(2) + 15 = 55
n = 20(3) + 15 = 75

We can see that all the values of n are divisible by 5 so the answer is 5.

\(n = { 15 , 35 , 55 , 75 , 95.........}\)

Check carefully, all the numbers are divisible by 5, Hence answer must be (B)
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FYI, there is an error in some of the solutions above which have been highlighted. The above solutions which used algebra to solve (like the one quoted below), actually made a mistake in their algebra.

They all solved to: n = 20q + 15

It should actually be n = 20q + 300

Because:
n/ 20 = q + 15 | multiplying both sides by 20 results in
n = 20 (q + 15)

which is NOT 20q + 15.

They still got the right solution because obviously 300 is a multiple of 15, but I would hate if someone made an algebra mistake on another question because of the error here.