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

Redeem

gs 1

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Master | Next Rank: 500 Posts
Posts: 114
Joined: Thu Mar 27, 2008 3:21 am

gs 1

by thegmatbeater » Sat Jul 26, 2008 6:17 am
John and Bill ara among 5 runners in arace 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
Top
Source: — Problem Solving |
Legendary Member
Posts: 829
Joined: Mon Jul 07, 2008 10:09 pm
Location: INDIA
Thanked: 84 times
Followed by:3 members

by sudhir3127 » Sat Jul 26, 2008 6:53 am
IMO D
Top
Junior | Next Rank: 30 Posts
Posts: 10
Joined: Tue Jun 17, 2008 7:36 am

by Chitts » Sat Jul 26, 2008 7:45 am
Is the anwser 10. I can explain if its correct
Regards,
Chitts
Top
Senior | Next Rank: 100 Posts
Posts: 75
Joined: Sun Jun 22, 2008 4:59 am
Thanked: 2 times

by dbart06 » Sat Jul 26, 2008 8:11 am
imo = 60
Top
Junior | Next Rank: 30 Posts
Posts: 10
Joined: Tue Jun 17, 2008 7:36 am

by Chitts » Sat Jul 26, 2008 8:22 am
if John finishes 1st bill can come 2nd,3rd, 4th, 5th. -- 4 ways
if john finishes 2nd bill can come 3rd, 4th, 5th -- 3 ways
if John finishes 3rd bill can come 4th, 5th -- 2
if John finishes 4th bill can come 5th -- 1

Total is 4+3+2+1 = 10..
Is this wrong?
Regards,
Chitts
Top
Legendary Member
Posts: 829
Joined: Mon Jul 07, 2008 10:09 pm
Location: INDIA
Thanked: 84 times
Followed by:3 members

by sudhir3127 » Sat Jul 26, 2008 8:35 am
i used a very simple approach ...

As there are 5 people there are 5! ways to arrange them
ie 120 ways to arrange them ...

So, in half of them one guy has to be ahead of the other and vice versa

that gives us 60 as answer..
Top
Master | Next Rank: 500 Posts
Posts: 139
Joined: Wed May 07, 2008 12:27 pm
Thanked: 8 times

by acecoolan » Sat Jul 26, 2008 9:00 am
Chitts wrote:if John finishes 1st bill can come 2nd,3rd, 4th, 5th. -- 4 ways
if john finishes 2nd bill can come 3rd, 4th, 5th -- 3 ways
if John finishes 3rd bill can come 4th, 5th -- 2
if John finishes 4th bill can come 5th -- 1

Total is 4+3+2+1 = 10..
Is this wrong?
Chitts ..you are just looking at the ways in which u can arrange these 2 persons ..u also need to look at the other peple. So add that ur logic

John is 1st - the remaining 4 people have 4! = 24 ways
John is 2nd - bill has 3 positions and the other people have 3! - hence 3! * 3 = 18
John is 3rd - bill has 2 postns and others have 3!, hence 3! * 2 = 12
John is 4th - bill has 1 postn and others 3!, hence 3! * 1 = 6

Add all 24 + 18 + 12 + 6 = 60

But Sudhir's approach is faster and a more intelligent way ..
Top
Legendary Member
Posts: 661
Joined: Tue Jul 08, 2008 12:58 pm
Location: France
Thanked: 48 times

by pepeprepa » Sat Jul 26, 2008 9:20 am
The problem is: How many ways
Either you understand ways as the number of possibilities of the whole runners
Or you understand as the different possibilities of ranking of the two guys (1st and 3rd / 1st and 2nd .....)
Top
User avatar
Legendary Member
Posts: 566
Joined: Fri Jan 04, 2008 11:01 am
Location: Philadelphia
Thanked: 31 times
GMAT Score:640

by AleksandrM » Sat Jul 26, 2008 11:06 am
5!/2!(5 - 2)! = 10

John has to come in ahead of Bill. The places are:

5 4 3 2 1

This means that John can come in ahead of Bill in the following ways.

5 4

5 3

5 2

5 1

4 3

4 2

4 1

3 2

3 1

2 1

Add them up, and you get 10 ways.
Top
Master | Next Rank: 500 Posts
Posts: 139
Joined: Wed May 07, 2008 12:27 pm
Thanked: 8 times

by acecoolan » Sat Jul 26, 2008 1:51 pm
So what is the OA for this ?

I agree pepeprepa - so am not sure how to intepret the question then
Top
Post new topic Post Reply
• Page 1 of 1