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Question

In a jar there are 21 white balls, 24 green balls and 32 blue balls. How many balls must be taken out in order to make sure we have 23 balls of the same color?

I read past threads regarding this kind of Qs but still can not understand.. is thr any formula for this kind of Q?

cans · Answer

21+44+1 = 66.
21 because its possible that first 21 balls are white and thus we can't get 23. next 44 because in case we get 22 green and 22 blue. still not 23. the next will surely either be green or blue. thus 23 same color..

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Cans!!

Brent@GMATPrepNow · Answer

mehrasa wrote:In a jar there are 21 white balls, 24 green balls and 32 blue balls. How many balls must be taken out in order to make sure we have 23 balls of the same color?

I read past threads regarding this kind of Qs but still can not understand.. is thr any formula for this kind of Q?

We can first reword the question to ask "What is the greatest number of balls that can be removed without getting 23 balls of the same color"

Well, we can remove 21 white balls, 22 green balls and 22 blue balls (65 balls so far).
At this point, if we remove one more ball (bringing the count to 66), we will be guaranteed to have 23 balls of the same color.

So, the answer is 66 balls.

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

mehrasa · Answer

now my question is that if there were 22 or 23 while balls in the jar instead of 21, the problem was solved like this:
22+22+22+1= 67

Brent@GMATPrepNow wrote:
mehrasa wrote:In a jar there are 21 white balls, 24 green balls and 32 blue balls. How many balls must be taken out in order to make sure we have 23 balls of the same color?

I read past threads regarding this kind of Qs but still can not understand.. is thr any formula for this kind of Q?
We can first reword the question to ask "What is the greatest number of balls that can be removed without getting 23 balls of the same color"

Well, we can remove 21 white balls, 22 green balls and 22 blue balls (65 balls so far).
At this point, if we remove one more ball (bringing the count to 66), we will be guaranteed to have 23 balls of the same color.

So, the answer is 66 balls.

Cheers,
Brent

Brent@GMATPrepNow · Answer

now my question is that if there were 22 or 23 while balls in the jar instead of 21, the problem was solved like this: 22+22+22+1= 67 Exactly. Cheers, Brent

Brent@GMATPrepNow · Answer

is thr any formula for this kind of Q?

Not sure how useful this will be but . . .

Let's say a jar contains a balls of one color, b balls of another color, c balls of another ...(and so on), where a, b, c, . . . are all greater than z. And let's say that there are k different colors altogether. Then the number of balls that must be removed in order to guarantee that we have z balls of the same color will be k(z-1)+1

Aside: I don't think there's much value in memorizing this formula. It's much better to understand how the solution works.

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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