Last visit was: 24 Apr 2026, 22:45 It is currently 24 Apr 2026, 22:45
Home
Messages
Tests
Schools
Events
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
Back to Forum
Create Topic
User avatar
GMATBusters
User avatar
GMAT Tutor
Joined: 27 Oct 2017
Last visit: 23 Apr 2026
Posts: 1,922
Own Kudos:
6,856
 [14]
Given Kudos: 241
WE:General Management (Education)
Expert
Expert reply
Posts: 1,922
Kudos: 6,856
 [14]
In how many ways 10 Oranges be distributed among 2 children if both mu 03 Nov 2018, 10:18
Kudos
Add Kudos
14
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

65% (hard)

Question Stats:

61% (02:27) correct 39% (02:31) wrong based on 167 sessions

History

Date
Time
Result
Not Attempted Yet
In how many ways 10 Oranges be distributed among 2 children if both must get odd no of Oranges?
A. 513
B. 540
C. 512
D. 515
E. 516

Weekly Quant Quiz #7 Question No 9

ShowHide Answer
Official Answer
C
Most Helpful Reply
User avatar
GMATBusters
User avatar
GMAT Tutor
Joined: 27 Oct 2017
Last visit: 23 Apr 2026
Posts: 1,922
Own Kudos:
6,856
 [5]
Given Kudos: 241
WE:General Management (Education)
Expert
Expert reply
Posts: 1,922
Kudos: 6,856
 [5]
In how many ways 10 Oranges be distributed among 2 children if both mu 05 Nov 2018, 02:08
5
Kudos
Add Kudos
Bookmarks
Bookmark this Post
sonusaini1

Total no of ways in which the 10 Oranges be given to 2 person = 2*2*2*…2 = 2^10

Now, there can only be two possibilities, either both get odd no of oranges or equal no of oranges. ( As the total no of oranges = even: Even = odd+odd or even +even)

Also the probability of both cases are equal = ½

Hence, the number of ways in which both received odd no of oranges = ½ * (Total no of ways ) = ½ * 2^10 = 2^9 = 512
General Discussion
User avatar
pk123
User avatar
Joined: 16 Sep 2011
Last visit: 26 Apr 2020
Posts: 104
Own Kudos:
122
 [3]
Given Kudos: 158
Products:
My Reviews
Posts: 104
Kudos: 122
 [3]
In how many ways 10 Oranges be distributed among 2 children if both mu 03 Nov 2018, 10:54
2
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
In how many ways 10 Oranges be distributed among 2 children if both must get odd no of apples?
A. 513
B. 540
C. 512
D. 515
E. 516

lets say (1,9) or (3,7) or (5,5) , (7,3) and (9,1)

so 10C1*9C9 +10C3*7C7+ 10C5*5C5+10C7*3C3+10C9*1C1
=10 + 10*9*8/3*2. + 10*9*8*7*6/ (5*4*3*2). + 10*9*8/(3*2) +10
=10+120+ 2*9*7*2+ 10*3*4 +10
=10+120+36*7+120+10
=10+120+252+120+10
=260+252=512

Option C is the answer
User avatar
nitesh50
User avatar
Current Student
Joined: 04 Jun 2018
Last visit: 09 Aug 2021
Posts: 135
Own Kudos:
69
 [1]
Given Kudos: 139
GMAT 1: 690 Q50 V32
GMAT 2: 710 Q50 V36
GMAT 3: 610 Q48 V25
GMAT 3: 610 Q48 V25
Posts: 135
Kudos: 69
 [1]
In how many ways 10 Oranges be distributed among 2 children if both mu 03 Nov 2018, 10:58
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
In how many ways 10 Oranges be distributed among 2 children if both must get odd no of apples?
A. 513
B. 540
C. 512
D. 515
E. 516


The children must get odd number of apples.

So If A gets 1 B can Get (3,5,7,9)
Similarly we get 4 cases ie 4^4

since there are 2 children we can multiply it by 2.

So ans:256*2: 512 C
avatar
SUNILAA
avatar
Joined: 09 Apr 2018
Last visit: 21 Nov 2021
Posts: 26
Own Kudos:
6
Given Kudos: 92
Location: India
Schools: IIMA PGPX"20
GPA: 3.5
Schools: IIMA PGPX"20
Posts: 26
Kudos: 6
In how many ways 10 Oranges be distributed among 2 children if both mu 03 Nov 2018, 12:58
Kudos
Add Kudos
Bookmarks
Bookmark this Post
ans is 515
9 1------- 10C9*9C1
7 3-------10C7*9C3
5 5--------10C5*9C5
3 7
1 9 add all
User avatar
saukrit
User avatar
Joined: 05 Jul 2018
Last visit: 23 Apr 2026
Posts: 378
Own Kudos:
425
 [1]
Given Kudos: 326
Status:Current student at IIMB
Affiliations: IIM Bangalore
Location: India
Concentration: General Management, Technology
Schools: IIMB EPGP'22 (A)
GMAT 1: 600 Q47 V26
GRE 1: Q162 V149
GPA: 3.6
WE:Information Technology (Consulting)
Products:
My Reviews
Schools: IIMB EPGP'22 (A)
GMAT 1: 600 Q47 V26
GRE 1: Q162 V149
Posts: 378
Kudos: 425
 [1]
In how many ways 10 Oranges be distributed among 2 children if both mu 03 Nov 2018, 21:47
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Only possible number of fruits that may be given is 1,3,5,7,9

So
Number of ways to select 1 fruit for 1st child & 9 fruits to second child is : 10C1*9C9
Number of ways to select 3 fruit for 1st child & 7 fruits to second child is :10C3*7C7
Number of ways to select 5 fruit for 1st child & 5 fruits to second child is :10C5*5C5
Number of ways to select 7 fruit for 1st child & 3 fruits to second child is :10C7*3C3
Number of ways to select 9 fruit for 1st child & 1 fruits to second child is :10C9*1C1
Total = \(10C1*9C9 + 10C3*7C7 + 10C5*5C5 + 10C7*3C3 + 10C9*1C1\\
=10 + 10*9*8/3*2. + 10*9*8*7*6/ (5*4*3*2). + 10*9*8/(3*2) +10\\
=10+120+ 2*9*7*2+ 10*3*4 +10\\
=10+120+36*7+120+10\\
=10+120+252+120+10\\
=260+252=512\)

Hence Option C is the answer
User avatar
saukrit
User avatar
Joined: 05 Jul 2018
Last visit: 23 Apr 2026
Posts: 378
Own Kudos:
425
Given Kudos: 326
Status:Current student at IIMB
Affiliations: IIM Bangalore
Location: India
Concentration: General Management, Technology
Schools: IIMB EPGP'22 (A)
GMAT 1: 600 Q47 V26
GRE 1: Q162 V149
GPA: 3.6
WE:Information Technology (Consulting)
Products:
My Reviews
Schools: IIMB EPGP'22 (A)
GMAT 1: 600 Q47 V26
GRE 1: Q162 V149
Posts: 378
Kudos: 425
In how many ways 10 Oranges be distributed among 2 children if both mu 03 Nov 2018, 21:51
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Only possible number of fruits that may be given is 1,3,5,7,9

So
Number of ways to select 1 fruit for 1st child & 9 fruits to second child is : 10C1*9C9
Number of ways to select 3 fruit for 1st child & 7 fruits to second child is :10C3*7C7
Number of ways to select 5 fruit for 1st child & 5 fruits to second child is :10C5*5C5
Number of ways to select 7 fruit for 1st child & 3 fruits to second child is :10C7*3C3
Number of ways to select 9 fruit for 1st child & 1 fruits to second child is :10C9*1C1
Total =
\(10C1*9C9 + 10C3*7C7 + 10C5*5C5 + 10C7*3C3 + 10C9*1C1\)
\(=10 + 10*9*8/3*2. + 10*9*8*7*6/ (5*4*3*2). + 10*9*8/(3*2) +10\)
\(=10+120+ 2*9*7*2+ 10*3*4 +10\)
\(=10+120+36*7+120+10\)
\(=10+120+252+120+10\)
\(=260+252=512\)

Hence Option C is the answer
User avatar
pandeyashwin
User avatar
Joined: 14 Jun 2018
Last visit: 25 Jan 2019
Posts: 165
Own Kudos:
321
Given Kudos: 176
Posts: 165
Kudos: 321
In how many ways 10 Oranges be distributed among 2 children if both mu 04 Nov 2018, 03:00
Kudos
Add Kudos
Bookmarks
Bookmark this Post
(1,9) -> 2 ways -> 2* 10! / 1!9! = 20
(3,7) -> 2 ways -> 2* 10!/ 3!7! = 240
(5,5) -> 1 way -> 10!/5!5! = 252

Total 512
User avatar
surendrasaini1
User avatar
Joined: 15 Feb 2017
Last visit: 08 Jan 2026
Posts: 242
Own Kudos:
126
Given Kudos: 50
Location: India
Schools: Stern '26
Schools: Stern '26
Posts: 242
Kudos: 126
In how many ways 10 Oranges be distributed among 2 children if both mu 05 Nov 2018, 01:20
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Hi guys

Is there any other way we can approach this problem.

Thanks

Sent from my Lenovo K33a42 using GMAT Club Forum mobile app
User avatar
nitesh50
User avatar
Current Student
Joined: 04 Jun 2018
Last visit: 09 Aug 2021
Posts: 135
Own Kudos:
69
Given Kudos: 139
GMAT 1: 690 Q50 V32
GMAT 2: 710 Q50 V36
GMAT 3: 610 Q48 V25
GMAT 3: 610 Q48 V25
Posts: 135
Kudos: 69
In how many ways 10 Oranges be distributed among 2 children if both mu 05 Nov 2018, 06:00
Kudos
Add Kudos
Bookmarks
Bookmark this Post
gmatbusters
sonusaini1

Total no of ways in which the 10 Oranges be given to 2 person = 2*2*2*…2 = \(2^10\)

Now, there can only be two possibilities, either both get odd no of oranges or equal no of oranges. ( As the total no of oranges = even: Even = odd+odd or even +even)

Also the probability of both cases are equal = ½

Hence, the number of ways in which both received odd no of oranges = ½ * (Total no of ways ) = ½ *\(2^10\) = \(2^9\) = 512
Show more


Total no of ways in which the 10 Oranges be given to 2 person = 2*2*2*…2 = \(2^10\)

Can you explain this?

Also, shouldn't the question also mention that the oranges are distinct.
It could easily be inferred as similar oranges. IN this case, the answer would have been vastly different.
User avatar
GMATBusters
User avatar
GMAT Tutor
Joined: 27 Oct 2017
Last visit: 23 Apr 2026
Posts: 1,922
Own Kudos:
6,856
Given Kudos: 241
WE:General Management (Education)
Expert
Expert reply
Posts: 1,922
Kudos: 6,856
In how many ways 10 Oranges be distributed among 2 children if both mu 05 Nov 2018, 07:28
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Response to query 1:

Total no of ways in which the 10 Oranges be given to 2 person
First orange can be given to any of the two person, no of ways = 2
Second orange can be given to any of the two person, no of ways = 2
.
.
.
.Tenth orange can be given to any of the two person, no of ways = 2

total no of ways =
= 2*2*2*…2 = 2^10

Response to query 2:

Unless it is specifically mentioned that the tems are identical, they are taken as distinct.



nitesh50
gmatbusters
sonusaini1

Total no of ways in which the 10 Oranges be given to 2 person = 2*2*2*…2 = \(2^10\)

Now, there can only be two possibilities, either both get odd no of oranges or equal no of oranges. ( As the total no of oranges = even: Even = odd+odd or even +even)

Also the probability of both cases are equal = ½

Hence, the number of ways in which both received odd no of oranges = ½ * (Total no of ways ) = ½ *\(2^10\) = \(2^9\) = 512


Total no of ways in which the 10 Oranges be given to 2 person = 2*2*2*…2 = \(2^10\)

Can you explain this?

Also, shouldn't the question also mention that the oranges are distinct.
It could easily be inferred as similar oranges. IN this case, the answer would have been vastly different.
Show more
User avatar
bumpbot
User avatar
Non-Human User
Joined: 09 Sep 2013
Last visit: 04 Jan 2021
Posts: 38,978
Own Kudos:
1,117
Posts: 38,978
Kudos: 1,117
In how many ways 10 Oranges be distributed among 2 children if both mu 30 Sep 2024, 06:53
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Automated notice from GMAT Club BumpBot:

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

This post was generated automatically.
Moderators:
Bunuel
Math Expert
109818 posts
Krunaal
Tuck School Moderator
853 posts