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M21 q

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M21 q [#permalink] New post 14 Mar 2012, 15:29
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If a box contains 10 red pills, 5 blue pills, and 12 yellow pills, what is the least number of pills one must extract from the box to ensure that at least three pills of each color are among those extracted?


# 12
# 17
# 18
# 23
# 25


In the worst possible scenario, one will draw 22 pills without drawing a single blue pill. To make sure that there will be 3 blue pills among the extracted, one has to draw 3 more than 22 (i.e. 25).
The correct answer is E.

In this question, why do really have to consider the worst case scenario when the question is really asking the least number of pill that have to be extracted.....it can be 11, 18,etc....shouldn't this question really be asking for maximum number of pills that need to be extracted instead of asking for least number of pills (as per how the explanation is working it really seems it's asking for maximum number of pills)
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Re: M21 q [#permalink] New post 14 Mar 2012, 15:40
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Hi, there. I'm happy to give my 2 cents on this. :)

For this particular type of question --- the least number to ensure, to guarantee without a shadow of a doubt, then basically, yes, you have to consider the "worst case scenario", as you correctly did.

I will point out, though, this is not a very common GMAT question type --- in fact, I'm not sure I have every seen a question like this in any of the official material I have reviewed.

A much more GMAT-like question would be --- what's the probability of picking a blue and a yellow pill when you pick two pills? More challenging prompts -- (a) Pick two pills: what's the probability that they are different colors? (b) pick three pills: what's the probability that they are three different colors? Those are prompts that more resemble what I have seen in official material.

Does all this make sense? Let me know if you have any questions on what I've said.

Mike :)
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Re: M21 q [#permalink] New post 27 Mar 2012, 00:47
Any no <25 doesn't guarantee the condition will occur.

e.g you calculate 18 with 5+10 +3 (yellow pills)

but while drawing 18 pills it may happn that 12 yellow pills and 6 red pills come out.

Hence it should be E (worst case.)
Re: M21 q   [#permalink] 27 Mar 2012, 00:47
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