BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

21 white balls, 24 green balls and 32 blue balls

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
User avatar
Community Manager
Posts: 1048
Joined: Mon Aug 17, 2009 3:26 am
Location: India
Thanked: 51 times
Followed by:27 members
GMAT Score:670

21 white balls, 24 green balls and 32 blue balls

by arora007 » Fri Jul 30, 2010 8:37 am
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 that we have 23 balls of the same color?
a) 23
b) 46
c) 57
d) 66
e) 67

Good question...
https://www.skiponemeal.org/
https://twitter.com/skiponemeal
Few things are impossible to diligence & skill.Great works are performed not by strength,but by perseverance

pm me if you find junk/spam/abusive language, Lets keep our community clean!!
Top
Source: — Problem Solving |
User avatar
Senior | Next Rank: 100 Posts
Posts: 55
Joined: Mon Sep 07, 2009 9:11 pm
Location: California
Thanked: 4 times

by nithi_mystics » Fri Jul 30, 2010 9:27 am
66 balls

21 white + 22 green + 23 blue or
21 white + 22 blue + 23 green
Thanks
Nithi
Top
Junior | Next Rank: 30 Posts
Posts: 18
Joined: Thu Aug 05, 2010 3:44 am

by rahul goyal » Mon Aug 09, 2010 11:57 pm
nithi_mystics wrote:66 balls

21 white + 22 green + 23 blue or
21 white + 22 blue + 23 green
Thanks Nithi.But give the explanation for clear idea.
Top
Senior | Next Rank: 100 Posts
Posts: 34
Joined: Thu Aug 05, 2010 2:39 am

by likithae » Tue Aug 10, 2010 2:39 am
nithi_mystics wrote:66 balls

21 white + 22 green + 23 blue or
21 white + 22 blue + 23 green
thanks.....but explain me clearly..... i can't understood your logic.......
Top
Junior | Next Rank: 30 Posts
Posts: 27
Joined: Tue Nov 10, 2009 2:29 pm
Thanked: 1 times

by anirban_lax » Tue Aug 10, 2010 9:00 am
The answer should be 66.
Here's how:
In solving this kind of problems we should consider the worst case scenario, i.e. what will make me draw more balls out of the jar or what will delay my process of getting 23 balls of the same color.
Note that we have only 21 white balls and hence can never have 23 white balls. Thus 21 white balls are there just to make your target worse ;)
Suppose you pick up the first 21 balls (if you are wondering how I decide on the number 21, note that we have only 21 white balls) and they all turn out to be white. Then you keep on picking balls but the next 21 turn out to be green; while the next 21 turn out to be blue. Thus after 21*3=63 draws you have 3 sets of 21 balls each of colors white, green and blue.
Now, we do not have anymore white balls, hence the next draw has to be blue or green. Suppose it's green while the subsequent draw is blue (remember you need to think about the worst case). So, we have 22 balls each of green and blue colors. One more ball will ensure that I have either 23 green or 23 blue balls.
Thus total number of draws from the jar is : 63 + 2 + 1 = 66

Hope this helps.

Thanks
Anirban
Top
Post new topic Post Reply
• Page 1 of 1