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# In a jar there are 15 white balls, 25 red balls, 10 blue balls and 20

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Manager
Joined: 22 Mar 2009
Posts: 77
Schools: Darden:Tepper:UCUIC:Kenan Flager:Nanyang:NUS:ISB:UCI Merage:Emory
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In a jar there are 15 white balls, 25 red balls, 10 blue balls and 20 [#permalink]

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02 Nov 2009, 10:59
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45% (medium)

Question Stats:

60% (01:02) correct 40% (01:12) wrong based on 178 sessions

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In a jar there are 15 white balls, 25 red balls, 10 blue balls and 20 green balls. How many balls must be taken out in order to make sure we took out 8 of the same color?

a) 8
b) 23
c) 29
d) 32
e) 53
[Reveal] Spoiler: OA

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Intern
Joined: 06 Oct 2009
Posts: 6
Re: In a jar there are 15 white balls, 25 red balls, 10 blue balls and 20 [#permalink]

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02 Nov 2009, 11:23
3
KUDOS
The question asks about how many balls MUST be taken out in order to make sure we took out 8 of the same color.

Now, in this case we have to be sure about our answer when we can say we have taken out 8 balls of same color.

Favorable case will be if we take out first eight balls and all of them are of the same color. But that is a favorable case and may not always be true.

A worst case will be when you are 100% sure that you have achieved the desired result.

As in this case: if you draw out first 28 balls and they are 7 of each color, W, R, B, G.
Now you know that any ball you take out next will be of any one of the above colors and hence you'll have 8 ball of same color.

So ans is 29.

I hope it's clear.
SVP
Joined: 29 Aug 2007
Posts: 2468
Re: In a jar there are 15 white balls, 25 red balls, 10 blue balls and 20 [#permalink]

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02 Nov 2009, 22:35
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kylexy wrote:
In a jar there are 15 white balls, 25 red balls, 10 blue balls and 20 green balls. How many balls must be taken out in order to make sure we took out 8 of the same color?

a) 8
b) 23
c) 29
d) 32
e) 53

Thats 29 in C.

I love these types of questions..
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Intern
Joined: 29 Jul 2009
Posts: 16
Re: In a jar there are 15 white balls, 25 red balls, 10 blue balls and 20 [#permalink]

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03 Nov 2009, 15:44
I don't get why there will be 7 of each when we draw out 28 balls. Could you please elaborate?
Manager
Joined: 12 Oct 2009
Posts: 248
Re: In a jar there are 15 white balls, 25 red balls, 10 blue balls and 20 [#permalink]

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04 Nov 2009, 05:08
Arora2m this one is for you :

Black Blue Yellow Green
1 1 1 1
1 1 1 1
.
.
.
.
.

similar pattern 7 times. the next ball will have to be from either of the colors and making the total tally of that color to 8 balls
Intern
Joined: 25 Oct 2009
Posts: 12
Re: In a jar there are 15 white balls, 25 red balls, 10 blue balls and 20 [#permalink]

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05 Nov 2009, 08:39
HI where do we come across these type of questions in og 11.If you could point out the question numbers it will be really greatful asap.
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Re: In a jar there are 15 white balls, 25 red balls, 10 blue balls and 20 [#permalink]

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12 May 2011, 03:12
nice question.

take 7 out of each color.7*4 + 1 = 29
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Joined: 09 Sep 2013
Posts: 14140
Re: In a jar there are 15 white balls, 25 red balls, 10 blue balls and 20 [#permalink]

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12 May 2016, 09:59
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Hello from the GMAT Club BumpBot!

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Joined: 02 Sep 2009
Posts: 43387
Re: In a jar there are 15 white balls, 25 red balls, 10 blue balls and 20 [#permalink]

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12 May 2016, 14:02
Expert's post
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kylexy wrote:
In a jar there are 15 white balls, 25 red balls, 10 blue balls and 20 green balls. How many balls must be taken out in order to make sure we took out 8 of the same color?

a) 8
b) 23
c) 29
d) 32
e) 53

Check other Worst Case Scenario Questions from our Special Questions Directory to understand the concept better.
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Manager
Status: IF YOU CAN DREAM IT, YOU CAN DO IT
Joined: 03 Jul 2017
Posts: 186
Location: India
Re: In a jar there are 15 white balls, 25 red balls, 10 blue balls and 20 [#permalink]

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09 Jul 2017, 21:25
Can someone please elaborate the concept in this question. Why do we have to consider each ball of different color??
Director
Joined: 13 Mar 2017
Posts: 561
Location: India
Concentration: General Management, Entrepreneurship
GPA: 3.8
WE: Engineering (Energy and Utilities)
Re: In a jar there are 15 white balls, 25 red balls, 10 blue balls and 20 [#permalink]

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09 Jul 2017, 22:00
kylexy wrote:
In a jar there are 15 white balls, 25 red balls, 10 blue balls and 20 green balls. How many balls must be taken out in order to make sure we took out 8 of the same color?

a) 8
b) 23
c) 29
d) 32
e) 53

This is a very simple question.
Jar contains 15 WB, 25 RB, 10 BB, 20 GB.

Now to ensure that there must be 8 balls of same colour,
the best case will be, we take out 8 ball of same colour &
the worst case will be when we take out 7 balls of each colours and then we take out any ball.
The last ball's colour will be the colour of the 8 balls with same colour and other 7 balls will be of their respective colour.

So to ensure that we have 8 balls of same colour we need to take out 7+7+7 +8 = 29 balls.

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Re: In a jar there are 15 white balls, 25 red balls, 10 blue balls and 20 [#permalink]

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12 Jul 2017, 16:05
kylexy wrote:
In a jar there are 15 white balls, 25 red balls, 10 blue balls and 20 green balls. How many balls must be taken out in order to make sure we took out 8 of the same color?

a) 8
b) 23
c) 29
d) 32
e) 53

The worst case scenario would be having to draw 7 balls of each color so that we wouldn’t have 8 balls of any one color. However, if we were to remove just one more ball, regardless of the color, we would then have 8 balls of one color. Thus, we need to remove 7 x 4 + 1 = 29 balls.

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Re: In a jar there are 15 white balls, 25 red balls, 10 blue balls and 20   [#permalink] 12 Jul 2017, 16:05
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