Hi LUANDATO,

We're told that A, B, C and D are positive integers, A/B gives us a remainder of 9 and C/D gives us a remainder of 5. We're asked which of the following is NOT a possible value for B+D. This is a great 'concept question' - and you can solve it without doing much math IF you understand the concept that this question is built around.

When dealing with remainders, the possible value of the remainder is 'limited' by what the denominator is. For example:

If you divide an integer by 2, then the ONLY possible remainders will be 0 and 1. (re: 2/2 = 1r0 and 3/2 = 1r1, then the cycle repeats).
If you divide an integer by 3, then the ONLY possible remainders will be 0, 1 and 2. (re: 3/3 = 1r0 and 4/3 = 1r1 and 5/3 = 1r2 then the cycle repeats).
Etc.

The pattern is that the largest possible remainder will be '1 LESS' than the denominator. We can use that concept 'in reverse' to answer this question.

Here, in one calculation we're getting a remainder of 9 (so the denominator must be AT LEAST 10) and in the other calculation we're getting a remainder of 5 (so the denominator must be AT LEAST 6). Thus, the minimum value of B+D is 10+6 = 16. Therefore, 15 is NOT a possible value.

Final Answer: E

GMAT assassins aren't born, they're made,
Rich