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Counting problem

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by bia » Wed May 07, 2008 6:21 am
The box contains 10 red pills, 5 blue pills, and 132 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 the extracted?
A. 12
B. 17
C. 18
D. 23
E. 25
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by akshatsingh » Wed May 07, 2008 10:05 pm
I think 18. As the question ask me to be really sure of getting 3 ball of each colour.

Is the answer C ?
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by rey.fernandez » Wed May 07, 2008 10:09 pm
I assume there was a typo in your post... and that there are 12 yellow pills, not 132.

That said, one way to approach this problem is to go through the answer choices, starting with the smallest and working your way up, imagining the worst case scenario.


A: 12 is not enough, since it's possible that all 12 could be yellow
B: 17 could be 12 yellow, 5 red... not enough
C: 18 could be 12 yellow, 6 red... not enough
D: 23 could be 12 yellow, 10 red, 1 blue... not enough
E: 25, that's gotta be it by elimination (12 yellow, 10 red, 3 blue)
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Re: Counting problem

by simplyjat » Wed May 07, 2008 10:09 pm
bia wrote:The box contains 10 red pills, 5 blue pills, and 132 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 the extracted?
A. 12
B. 17
C. 18
D. 23
E. 25
Can you check the count for yellow pills? If there are 132 yellow pills none of the answer choices make any sense
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by VP_RedSoxFan » Thu May 08, 2008 5:01 am
Ditto, to ENSURE that you get one of each given the pill counts you list, then the answer would be 145. The question must have read, as has been stated, 12 yellow pills. If that is the case, the answer is 25 as rey gives a good, concise explanation.
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by Stuart@KaplanGMAT » Thu May 08, 2008 10:46 am
rey.fernandez wrote:I assume there was a typo in your post... and that there are 12 yellow pills, not 132.

That said, one way to approach this problem is to go through the answer choices, starting with the smallest and working your way up, imagining the worst case scenario.


A: 12 is not enough, since it's possible that all 12 could be yellow
B: 17 could be 12 yellow, 5 red... not enough
C: 18 could be 12 yellow, 6 red... not enough
D: 23 could be 12 yellow, 10 red, 1 blue... not enough
E: 25, that's gotta be it by elimination (12 yellow, 10 red, 3 blue)
Great approach!

We also could have predicted the answer.

In this type of question, we always want to consider worst case scenarios. In other words, what could happen to stop us from getting 3 of each colour?

Well, we could start by picking all 12 yellow pills. Then, if we got unlucky, we'd pick all 10 blue pills. Now there's nothing left but red, so the next 3 have to be red pills.

So, 12 + 10 + 3 = 25.
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by bia » Thu May 08, 2008 3:48 pm
The question seems to be incorrect. It must have been 12 yellow pills. Thanks for your answers.
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