A combined of 55 light bulbs are stored in two boxes; of these, a tota

Question

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.

Bunuel · Accepted Answer

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?

Since there are 2 broken bulbs in the first box then there are 5 broken bulbs in the second box.

(1) In the first box, the number of bulbs that are not broken is 15 times the number of the broken bulbs --> say # of bulbs in the first box is x, then x-2=15*2 --> x=32 --> there are 55-32=23 bulbs in the second box out of which 23-5=18 are not broken. Sufficient.

(2) The total number of bulbs in the first box is 9 more than the total number of bulbs in the second box --> say # of bulbs in the second box is y, then # of bulbs in the first box is y+9 --> (y+9)+y=55 --> y=23. Sufficient.

Answer: D.

krrish · Answer

Stmt1: Box 1 had 32 bulbs -> B2 had 23 so A suff
stmt2: B1 = B2+9 = > 2(B2)+9 =55 so, B2 and B1 values can be determined, also given 2 Broken bulbs are in B1 so rest of them in B2, now bustract the rest from B2 which gives the no of non broken bulbs

hence D is suff

anairamitch1804 · Answer

We are asked for the number not broken in the second box. We know there are 55 bulbs in total and that 7 of them are broken. We know there are 2 broken in the first box, and 5 broken in the second box, (and that the other 48 remaining bulbs are not broken.)

We will be able to compute the number of not broken in the second box if we know the total number in the second box...or if we know the total number in the first box...and, finally, because we know that the total is 55, we will also have sufficiency if we get a special equation relating the total number in the first box to the total number in the second box.

Statement 2: this is a special equation that will allow us to compute the total number in the second box. Once we have that, we would simply subtract the 5 broken, and we'd have the number not broken in the second box. But because this is data sufficiency, instead of actually doing that math, we would just realize (after/during our analysis) that we COULD do it.

So here's the work we wouldn't actually do:

# in 1st box + # in 2nd box =55 (from question)
# in 1st box = # in 2nd box + 9 (statement 2)

subbing in:

(# in 2nd box + 9) + # in 2nd box =55

solving:
# in 2nd box = 23
Therefore, number of not broken in 2nd box is 23-5= 18
Sufficient.

Hence D.

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A combined of 55 light bulbs are stored in two boxes; of these, a tota

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GMAT Data Sufficiency (DS) Questions

A combined of 55 light bulbs are stored in two boxes; of these, a tota

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