Red, blue and yellow pills

[rahulvsd]

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?

A)12
B)17
C)18
D)23
E)25

[spoiler]OA: E[/spoiler]

[sam2304]

For a minimum of 3 pills of each color, consider the worst case scenario.

Here the worst case scenario is first you pick all the 12 yellow pills as they contribute the maximum no of pills among all. Then comes 10 red pills then another 3 for blue. Now will have a minimum of 3 pills in each color. Hence E.

[GMATGuruNY]

Here are two similar problems:

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https://www.beatthegmat.com/have-23-ball ... 83542.html

[shantanu86]

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?

A)12
B)17
C)18
D)23
E)25

[spoiler]OA: E[/spoiler]

Hi sam2304, rahulvsd,

I have another approach for the solution.
Lets start backwards,

If one draws all 27 balls 3 of each color are ensured.
Now, start removing the balls. Since blue colored ones are the least (=5) at max 2 balls can be removed from 27.

In worst case removing additional balls will cause blue balls to go bellow 3.
Hence answer is 25.. E

[ritzzzr]

The worst case would be if in first 12 chance i get all yellow ,then in next 10 chance i get all red (as my bad luck is helping me ) but after 22 chance i know the next one will be certainly the blue pill & for it to be 3 i need 3 chance....
sp total 25