BrainLab wrote:

If n is a positive integer, which one of the following numbers must have a remainder of 3 when

divided by any of the numbers 4, 5, and 6?

(A) 12n + 3

(B) 24n + 3

(C) 80n + 3

(D) 90n + 2

(E) 120n + 3

Source: GMAT Math Bible

Out of the given options, the correct answer will be the one having the divisor a multiple of 4,5,6 in order for all 3 of these give the same remainder.

LCM of 4,5,6 = 60.

Out of the given options only option E can be written in the form of multiple of 60 for the divisor as 2*60*n+3

E is thus the correct answer.

Hope this helps.