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A number of ties are individually packaged in unmarked boxes

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A number of ties are individually packaged in unmarked boxes

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A number of ties are individually packaged in unmarked boxes. What is the maximum number of boxes that must be opened if boxes are opened at random until there are three open boxes containing ties of the same color?

1) There are five distinct colors of ties.
2) There are 25 boxes.

OA A

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It makes no logical sense to ask a DS question like this, because it's not clear what information would be sufficient to find the "maximum number" of something. That's easy to see if you imagine a different question:

There are 25 boxes, and each box contains one colored tie. What is the maximum number of boxes that must be opened until three open boxes contain ties of the same color?
1. There are 5 different colors of tie.
2. 21 boxes contain a red tie

Using Statement 1 alone, we might open ten boxes and still only have five pairs of colored ties, but once we open box #11, we must get three of the same color. So it might seem that Statement 1 is sufficient, and the answer is 11. But then look at Statement 2: if 21 have red ties, then even if we open the other four boxes first, once we open the next three boxes we are guaranteed to have three red ties. So it might now seem the answer is 7. So which statement is sufficient? Is the answer D, or is it B, or is it maybe C because using Statement 2 alone, it's possible we only have two different colors of tie, and then the maximum would be 5? There is no good answer choice because a question like this is completely illogical: there is no way to tell what kind of information is sufficient to answer it.

They clearly intend Statement 1 to be sufficient, since with five colors, opening 11 boxes ensures you have three of a kind, but you could never see a question set up this way on the GMAT. I think E is just as justifiable an answer as A here, since with no information about the distribution of colors, you can't be sure if the maximum is truly 11 or if it might be less than 11 (as in the case where 21 boxes contain red ties).

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