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In a jar there are 21 white balls, 24 green balls and 32

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In a jar there are 21 white balls, 24 green balls and 32 [#permalink]

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New post 01 Aug 2014, 01:52
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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?

a) 23
b) 46
c) 57
d) 66
e) 67
[Reveal] Spoiler: OA

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Re: In a jar there are 21 white balls, 24 green balls and 32 [#permalink]

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New post 01 Aug 2014, 02:02
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LucyDang 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?

a) 23
b) 46
c) 57
d) 66
e) 67



Here, we need to find minimum number of marbles to be taken out to get 23 marbles of same color.

For a instance, if we take 21 white marbles 1st and followed by 22 Green and then 22 Blue.

Total will be 21 + 22+ 22= 65 draws.

If we choose either Green or Blue next time. This will bring the total of either of these colored marble to 23.

So Minimum we need to take 65+1 = 66 Times to get 23 marbles of same color(either Green or Blue).

Answer : D.

Hope it helps.
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Re: In a jar there are 21 white balls, 24 green balls and 32 [#permalink]

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LucyDang 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?

a) 23
b) 46
c) 57
d) 66
e) 67


To ensure that we have 23 balls of the same color, we should consider the worst case scenario.

The worst case scenario would be if we take 21 white balls, 22 green balls and 22 blue balls. In this case we won't have 23 balls of the same color. After that, there will be only green and blue balls left in the jar and no matter which one we take next we'll have either 23 green or 23 blue balls. So, the minimum number of balls we should pick is 21 + 22 + 22 + 1 = 66.

Answer: D.

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Hope it helps.
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Re: In a jar there are 21 white balls, 24 green balls and 32 [#permalink]

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New post 06 Aug 2014, 04:07
I think the trick is in the scope shifting so 23 of one colour can be either in the jar by removing other marbles or outside the jar as a result of being moved out.

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Re: In a jar there are 21 white balls, 24 green balls and 32 [#permalink]

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New post 16 Jan 2015, 13:52
The answer is 23.

Remember? The balls are in a jar. Jars are made of glass so you can see the colors of the ones that you wanted to take out.

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Re: In a jar there are 21 white balls, 24 green balls and 32 [#permalink]

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New post 28 Oct 2015, 18:36
very tricky, and the wording is confusing.

23 of the same color must be left in the jar or outside?
if in the jar, then we need to take at least 21 out + 1 green and 32 blue or 21 white 24 green and 9 blue. but neither works, so it must be the case that we need to take out, and see if we have at least 23 of the same kind.
to make sure that we have 23 of the same kind, we need to take 21 white, 23 blue or green and 22 blue or green. this gives us a total of 66.
what is the source of this question?

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Re: In a jar there are 21 white balls, 24 green balls and 32 [#permalink]

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New post 28 Oct 2015, 22:17
mvictor wrote:
very tricky, and the wording is confusing.

23 of the same color must be left in the jar or outside?
if in the jar, then we need to take at least 21 out + 1 green and 32 blue or 21 white 24 green and 9 blue. but neither works, so it must be the case that we need to take out, and see if we have at least 23 of the same kind.
to make sure that we have 23 of the same kind, we need to take 21 white, 23 blue or green and 22 blue or green. this gives us a total of 66.
what is the source of this question?


Actually, the wording of the question is quite standard. How many do you need to take out to ensure that you have 23 of the same colour? means that out of the balls taken out, we need to ensure that there should be 23 of the same colour.
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Re: In a jar there are 21 white balls, 24 green balls and 32 [#permalink]

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New post 16 Apr 2017, 00:32
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Re: In a jar there are 21 white balls, 24 green balls and 32   [#permalink] 16 Apr 2017, 00:32
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