NEW HERE? LEARN MORE
closeclose
Last visit was: 26 Apr 2024, 01:11 It is currently 26 Apr 2024, 01:11
Decision Tracker
My Rewards
New posts
New comers' posts

Close
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel

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

SORT BY:
Date
Kudos
Tags:
Find Similar Topics 
Show Tags
Hide Tags
User avatar
B
LucyDang
Manager
Manager
Joined: 24 Mar 2010
Posts: 57
Own Kudos [?]: 384 [48]
Given Kudos: 105
Send PM
GMAT ToolKit User
In a jar there are 21 white balls, 24 green balls and 32 [#permalink] New post   01 Aug 2014, 01:52
3
Kudos
45
Bookmarks
00:00
A
B
C
D
E

Difficulty:

55% (hard)

Question Stats:

58% (01:32) correct 42% (02:03) wrong based on 659 sessions
Hide Show timer Statistics
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
ShowHide Answer
Official Answer
D
Most Helpful Reply
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92921
Own Kudos [?]: 619088 [14]
Given Kudos: 81596
Send PM
CAT Tests Forum Quiz Mode
Re: In a jar there are 21 white balls, 24 green balls and 32 [#permalink] New post   01 Aug 2014, 07:18
5
Kudos
9
Bookmarks
Expert Reply
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.

Similar questions to practice:
12-easy-pieces-or-not-126366.html#p1033935
in-his-pocket-a-boy-has-3-red-marbles-4-blue-marbles-and-85216.html
of-the-science-books-in-a-certain-supply-room-50-are-on-131100.html
in-a-deck-of-52-cards-each-card-is-one-of-4-different-color-83183.html
a-box-contains-10-red-pills-5-blue-pills-12-yellow-56779.html
each-of-the-integers-from-0-to-9-inclusive-is-written-on-130562.html
a-student-is-asked-to-pick-marbles-from-a-bag-that-contains-72390.html
of-the-science-books-in-a-certain-supply-room-50-are-on-131100.html
if-a-librarian-randomly-removes-science-books-from-a-library-93861.html
each-of-the-integers-from-0-to-9-inclusive-is-written-on-130562.html
a-box-contains-10-tablets-of-medicine-a-and-15-tablets-157726.html
there-are-12-red-balls-10-blue-balls-15-red-balls-and-134437.html

Hope it helps.
User avatar
P
Gnpth
VP
VP
Joined: 29 Aug 2012
Status:Chasing my MBB Dream!
Posts: 1057
Own Kudos [?]: 6255 [5]
Given Kudos: 330
Location: United States (DC)
WE:General Management (Aerospace and Defense)
Send PM
GMAT ToolKit User Reviews Badge
Re: In a jar there are 21 white balls, 24 green balls and 32 [#permalink] New post   01 Aug 2014, 02:02
5
Kudos
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.
General Discussion
avatar
himanshujovi
Manager
Manager
Joined: 28 Apr 2014
Posts: 141
Own Kudos [?]: 74 [1]
Given Kudos: 46
Send PM
GMAT ToolKit User
Re: In a jar there are 21 white balls, 24 green balls and 32 [#permalink] New post   06 Aug 2014, 04:07
1
Kudos
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.
avatar
dstephens
Intern
Intern
Joined: 16 Jan 2015
Posts: 1
Own Kudos [?]: 1 [0]
Given Kudos: 0
Send PM
Re: In a jar there are 21 white balls, 24 green balls and 32 [#permalink] 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.
User avatar
P
mvictor
Board of Directors
Joined: 17 Jul 2014
Posts: 2163
Own Kudos [?]: 1180 [0]
Given Kudos: 236
Location: United States (IL)
Concentration: Finance, Economics
Schools: Stanford '20 (WD)
GMAT 1: 650 Q49 V30
GPA: 3.92
WE:General Management (Transportation)
Send PM
GMAT ToolKit User Reviews Badge
Re: In a jar there are 21 white balls, 24 green balls and 32 [#permalink] 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?
User avatar
L
KarishmaB
Tutor
Joined: 16 Oct 2010
Posts: 14823
Own Kudos [?]: 64926 [0]
Given Kudos: 426
Location: Pune, India
Send PM
Re: In a jar there are 21 white balls, 24 green balls and 32 [#permalink] New post   28 Oct 2015, 22:17
Expert Reply
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.
User avatar
L
AkshdeepS
VP
VP
Joined: 13 Apr 2013
Status:It's near - I can see.
Posts: 1479
Own Kudos [?]: 1603 [0]
Given Kudos: 1002
Location: India
Concentration: International Business, Operations
GPA: 3.01
WE:Engineering (Real Estate)
Send PM
Reviews Badge
Re: In a jar there are 21 white balls, 24 green balls and 32 [#permalink] New post   09 Apr 2019, 11:01
VeritasKarishma wrote:
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.


VeritasKarishma : Not able to understand what the question is asking and how to imagine this situation of marbles. :(

Please help.
User avatar
L
KarishmaB
Tutor
Joined: 16 Oct 2010
Posts: 14823
Own Kudos [?]: 64926 [2]
Given Kudos: 426
Location: Pune, India
Send PM
Re: In a jar there are 21 white balls, 24 green balls and 32 [#permalink] New post   09 Apr 2019, 21:25
1
Kudos
1
Bookmarks
Expert Reply
AkshdeepS wrote:
VeritasKarishma wrote:
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.


VeritasKarishma : Not able to understand what the question is asking and how to imagine this situation of marbles. :(

Please help.



Think about a simpler case.
Say you have a box with 2 red balls, 2 blue balls and 2 white balls. Now you need to take out some balls to ensure you have two fo the same colour. How many balls do you need to take out to ENSURE that you have 2 balls of same colour.
Say, you took out a red ball. Then a blue ball. Then a white ball. You still don't have 2 balls of same colour. Now the next ball you take out will make it two balls of same colour. So we need to take out 4 balls to ENSURE that there are 2 of the same colour.

This is the same case here. Now, review the original question and solution.
avatar
B
kunalbean
Intern
Intern
Joined: 01 Dec 2018
Posts: 34
Own Kudos [?]: 12 [0]
Given Kudos: 25
Send PM
Re: In a jar there are 21 white balls, 24 green balls and 32 [#permalink] New post   30 Jul 2019, 03:07
Gnpth wrote:
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.





Hi! Can you please explain that why are we taking only 22 marbles for Green? The worst case scenario will be when last 3 are of different color and the one we pick will result in all of same color. Hence, 21+23+23 - 3 + 1 = 65.
User avatar
P
sanjayparihar16
Manager
Manager
Joined: 12 Apr 2018
Posts: 170
Own Kudos [?]: 137 [0]
Given Kudos: 426
Send PM
Re: In a jar there are 21 white balls, 24 green balls and 32 [#permalink] New post   04 Jul 2020, 04:45
kunalbean wrote:
Gnpth wrote:
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.





Hi! Can you please explain that why are we taking only 22 marbles for Green? The worst case scenario will be when last 3 are of different color and the one we pick will result in all of same color. Hence, 21+23+23 - 3 + 1 = 65.


We are taking only 22 marbles for Green because 1 more marble would suffice our need i.e. 23 marbles of same colour. So we are trying to reach a case where we are just one short of a marble such that any marble pick would help in reaching the required condition.
User avatar
P
Crytiocanalyst
Director
Director
Joined: 16 Jun 2021
Posts: 994
Own Kudos [?]: 183 [0]
Given Kudos: 309
Send PM
Re: In a jar there are 21 white balls, 24 green balls and 32 [#permalink] New post   14 Aug 2021, 23:53
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 make sure we have 23 balls of the colour we have to adapt the pigeon hole stratergy

Take the number just below the given number that makes up these balls the number being 22

so that 21 balls from the first jar 22 from jar 2 and 3 respectively

and finally adding 1 ball just to make it 1 colour of 23

Therefore total =21+22*2+1= 66 hence D
User avatar
bumpbot
Non-Human User
Joined: 09 Sep 2013
Posts: 32679
Own Kudos [?]: 822 [0]
Given Kudos: 0
Send PM
Re: In a jar there are 21 white balls, 24 green balls and 32 [#permalink] New post   10 Jan 2024, 06:47
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
GMAT Club Bot
gmatclubot
Re: In a jar there are 21 white balls, 24 green balls and 32 [#permalink]
10 Jan 2024, 06:47
Moderators:
Bunuel
Math Expert
92918 posts
yashikaaggarwal
Senior Moderator - Masters Forum
3137 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne
Main navigation
GMAT Resources
Partners
MBA Resources
www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions