DS quesiton . please help

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silvia928: Senior | Next Rank: 100 Posts; Posts: 37; Joined: Sat May 24, 2008 8:59 pm

DS quesiton . please help

by silvia928 » Sun May 25, 2008 11:09 pm

4.) Meg and Bob are among the 5 participants in a cycling race. If each participant finishes the race and no two participants finish at the same time, in how many different possible orders can the participants finish the race so that Meg finishes ahead of Bob?

A. 24
B. 30
C. 60
D.90
E. 120

The answer is : C

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Source: Beat The GMAT — Data Sufficiency | Sun May 25, 2008 11:09 pm

getneonow: Senior | Next Rank: 100 Posts; Posts: 42; Joined: Fri Mar 14, 2008 1:56 am; Location: India; Thanked: 4 times; GMAT Score:730

by getneonow » Mon May 26, 2008 4:42 am

(1+2+3+4) * 3! = 60

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kausis: Newbie | Next Rank: 10 Posts; Posts: 9; Joined: Mon May 26, 2008 6:20 am; Thanked: 1 times

by kausis » Mon May 26, 2008 7:10 am

A slightly more detailed answer would be, since Meg finishes ahead of Bob, Meg can be at the 1st, 2nd, 3rd or 4th position (and not the last!).

So, if Meg is 1st, Bob can be in any one of the other 4 positions
-OR- (+)
if Meg is 2nd, Bob can be in any of the 3 next positions
-OR- (+)
---'' ---- 3rd, -------------------------'' --- 2 next positions
-OR- (+)
---'' ---- 4th, then Bob can be only at the last position (1 way)
-AND- (x)
the other three cyclists can be arranged in 3! ways.

Hence the final answer would be (4 + 3 + 2 + 1)x3! = 60 [C]

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Stuart@KaplanGMAT: GMAT Instructor; Posts: 3225; Joined: Tue Jan 08, 2008 2:40 pm; Location: Toronto; Thanked: 1710 times; Followed by:614 members; GMAT Score:800

Re: DS quesiton . please help

by Stuart@KaplanGMAT » Mon May 26, 2008 9:38 am

silvia928 wrote:4.) Meg and Bob are among the 5 participants in a cycling race. If each participant finishes the race and no two participants finish at the same time, in how many different possible orders can the participants finish the race so that Meg finishes ahead of Bob?

A. 24
B. 30
C. 60
D.90
E. 120

The answer is : C

A great first step would be figuring out that this is a problem solving question, not a data sufficiency one - please label your posts properly and put them in the proper section.