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

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BTGmoderatorDC: Moderator; Posts: 7187; Joined: Thu Sep 07, 2017 4:43 pmFollowed by: 23 members

by BTGmoderatorDC » Fri Jun 07, 2019 3:34 am

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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

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Source: Beat The GMAT — Data Sufficiency | Fri Jun 07, 2019 3:34 am

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Ian Stewart: GMAT Instructor; Posts: 2623; Joined: Mon Jun 02, 2008 3:17 amFollowed by: 355 members; Location: Montreal; Thanked: 1090 times; GMAT Score:780

by Ian Stewart » Fri Jun 07, 2019 7:37 am

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.

For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

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