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
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Hi BrainLab,

This question can be solved by TESTing VALUES and a bit of arithmetic.

We're told that N is a POSITIVE INTEGER. We're asked which of the following numbers MUST have a remainder of 3 when divided by any of the numbers 4, 5, and 6?

Let's TEST N=1

A) 12N + 3 = 15 --> 15/5 = 3r0. This is NOT a match
B) 24N + 3 = 27 --> 27/5 = 5r2. This is NOT a match
C) 80N + 3 = 83 --> 83/6 = 13r5. This is NOT a match
D) 90N + 2 = 92 --> 92/5 = 18r2. This is NOT a match

There's only one answer left...

Final Answer:

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4*5*6=120
E