Yesterday, Manhattan GMAT posted a GMAT question on our blog. Today, they have followed up with the answer:
The key to this problem is to translate the “game” into more familiar mathematical language. First of all, each bead’s color corresponds to a remainder after division by 5. For instance, Red = R0 (remainder of 0), which means that the number in question is a multiple of 5. Blue = R1, Green = R2, etc.
We withdraw four blues, three greens, two yellows, and an orange. In other words, we have four R1 numbers, three R2 numbers, two R3 numbers, and one R4 number.
If we want to, we can pick actual numbers. It would be best to pick small numbers—for instance, R1 could actually be 1, because when you divide 1 by 5, you get a quotient of 0 and a remainder of 1. Likewise, R2 could be 2, R3 could be 3, and R4 could be 4.
Multiplying these numbers together, we get 1x1x1x1x2x2x2x3x3x4 = 8x9x4 = 72×4 = 288. The remainder after division by 5 would be 3, and the color of the bead would be yellow. We would get the same result without picking numbers, of course—we would have to multiply the remainders together, which would give us R288, and then we’d reduce that to R3. Either way, we have a yellow bead.
The correct answer is D.