Last visit was: 25 Apr 2026, 06:01 It is currently 25 Apr 2026, 06:01
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
User avatar
puma
User avatar
Joined: 23 Mar 2008
Last visit: 11 Oct 2008
Posts: 153
Own Kudos:
1,620
Posts: 153
Kudos: 1,620
JOhn and Bill are among five runners in a race where there 17 Apr 2008, 12:20
Kudos
Add Kudos
Bookmarks
Bookmark this Post
JOhn and Bill are among five runners in a race where there are no ties. how many ways is it possible for John to finish the race ahead of Bill?

a) 5
b) 10
c) 30
d) 60
e) 120



Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Quantitative Questions Forum
Still interested in this question? Check out the "Best Topics" block below for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
avatar
malvika1979
avatar
Joined: 17 Apr 2008
Last visit: 17 Apr 2008
Posts: 1
Posts: 1
Kudos: 0
JOhn and Bill are among five runners in a race where there 17 Apr 2008, 12:32
Kudos
Add Kudos
Bookmarks
Bookmark this Post
i think the answer shud be 60 .
By the way wot is the answer
User avatar
walker
User avatar
Joined: 17 Nov 2007
Last visit: 25 May 2025
Posts: 2,396
Own Kudos:
10,847
Given Kudos: 362
Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
GMAT 1: 750 Q50 V40
Expert
Expert reply
Schools: Chicago (Booth) - Class of 2011
GMAT 1: 750 Q50 V40
Posts: 2,396
Kudos: 10,847
JOhn and Bill are among five runners in a race where there 17 Apr 2008, 12:38
Kudos
Add Kudos
Bookmarks
Bookmark this Post
D

1. All possible combinations: \(P^5_5=5!=120\)

2. Due to symmetry, all combinations can be evenly divided by two groups: John ahead of Bill and Bill ahead of John. So, \(N=\frac{120}{2}=60\)
User avatar
Sunchaser20
User avatar
Joined: 15 Apr 2008
Last visit: 28 Nov 2015
Posts: 28
Own Kudos:
32
Given Kudos: 8
Location: Moscow
Posts: 28
Kudos: 32
JOhn and Bill are among five runners in a race where there 17 Apr 2008, 15:11
Kudos
Add Kudos
Bookmarks
Bookmark this Post
puma
how many ways is it possible for John to finish the race ahead of Bill?
Show more

(B) for me. If I get the question right, we care only about John's and Bill's positions. Then we have:
J B 3 4 5
J 2 B 4 5
J 2 3 B 5
J 2 3 4 B

1 J B 4 5
1 J 3 B 5
....
i.e. 4+3+2+1 = 10 possible ways..
User avatar
dishant007
User avatar
Joined: 27 Mar 2008
Last visit: 29 Nov 2008
Posts: 40
Own Kudos:
15
Posts: 40
Kudos: 15
JOhn and Bill are among five runners in a race where there 17 Apr 2008, 16:03
Kudos
Add Kudos
Bookmarks
Bookmark this Post
For me:

J 4 3 2 1= 4!= 24

3 J 3 2 1= 3*3!= 9

which means it is greater than 30.

And 5! = 120, therefore it has to be less than 120.

Only 60 fits the bill.

Whats the OA/OE?
avatar
pmenon
avatar
Joined: 28 Dec 2005
Last visit: 01 Jul 2009
Posts: 691
Own Kudos:
620
Given Kudos: 2
Posts: 691
Kudos: 620
JOhn and Bill are among five runners in a race where there 17 Apr 2008, 18:28
Kudos
Add Kudos
Bookmarks
Bookmark this Post
im getting 10 as well, by just listing out the possibilities ...
User avatar
buffdaddy
User avatar
Joined: 14 Oct 2007
Last visit: 13 Jan 2011
Posts: 546
Own Kudos:
303
Given Kudos: 8
Location: Oxford
Schools:Oxford'10
Posts: 546
Kudos: 303
JOhn and Bill are among five runners in a race where there 17 Apr 2008, 23:32
Kudos
Add Kudos
Bookmarks
Bookmark this Post
If we care about the other participants' positions then the answer is 60 pointed out by walker,

if we dont (which is the case here) we have to divide this be 3! (the number of ways the others can finish).

so it is infact 60/6 = 10
User avatar
buffdaddy
User avatar
Joined: 14 Oct 2007
Last visit: 13 Jan 2011
Posts: 546
Own Kudos:
303
Given Kudos: 8
Location: Oxford
Schools:Oxford'10
Posts: 546
Kudos: 303
JOhn and Bill are among five runners in a race where there 18 Apr 2008, 12:40
Kudos
Add Kudos
Bookmarks
Bookmark this Post
puma
OA is D
Show more

this is so cruel :-)

hmm...i am a bit confused either way. On the one hand I am not sure if "how many ways is it possible for John to finish the race ahead of Bill" implies that the other runner's positions matter
User avatar
bkk145
User avatar
Joined: 10 Jun 2007
Last visit: 23 Feb 2014
Posts: 645
Own Kudos:
1,801
Posts: 645
Kudos: 1,801
JOhn and Bill are among five runners in a race where there 18 Apr 2008, 13:15
Kudos
Add Kudos
Bookmarks
Bookmark this Post
puma
JOhn and Bill are among five runners in a race where there are no ties. how many ways is it possible for John to finish the race ahead of Bill?

a) 5
b) 10
c) 30
d) 60
e) 120
Show more

D.

Layout the options
JBXXX = 4! = 24
XJBXX = 3*3! = 18
XXJBX = 2*3! = 12
XXXJB = 3! = 6

Total = 24+18+12+6 = 60



Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Quantitative Questions Forum
Still interested in this question? Check out the "Best Topics" block above for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!