A combined of 55 light bulbs are stored in two boxes; of the

[BTGmoderatorDC]

A combined of 55 light bulbs are stored in two boxes; of these, a total of 7 are broken. If there are exactly two broken bulbs in the first box, what is the number of bulbs in the second box that are not broken?

(1) In the first box, the number of bulbs that are not broken is 15 times the number of the broken bulbs.
(2) The total number of bulbs in the first box is 9 more than the total number of bulbs in the second box.

OA D

Source: GMAT Prep

[Ian Stewart]

We have 2 broken bulbs in the first box, so the rest of the 7 broken bulbs must be in the second box, and we have 5 broken bulbs in the second box.

From Statement 1, we have 30 unbroken bulbs in the first box, and thus 32 bulbs in total in that box. The rest of the bulbs are in the other box, so we have 55-32 = 23 bulbs in that box. If 5 of those are broken, the rest, 18 bulbs, are not, so Statement 1 is sufficient.

From Statement 2, if we have F bulbs in the first box in total, and S bulbs in the second box in total, we know

F+S = 55
F - S = 9

and if we just add these two equations, we find 2F = 64, so F = 32, and we have the same information as we had using Statement 1, so Statement 2 is also sufficient and the answer is D.