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Runners V, W, X, Y, and Z are competing in the Bayville local triathlo

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Joined: 02 Sep 2009
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Kudos [?]: 139576 [0], given: 12794

Runners V, W, X, Y, and Z are competing in the Bayville local triathlo [#permalink]

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New post 20 Dec 2017, 01:17
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Runners V, W, X, Y, and Z are competing in the Bayville local triathlon. If V finishes before W and W finishes before Z, how many ways can X finish before Y??

A. 5
B. 10
C. 30
D. 60
E. 120
[Reveal] Spoiler: OA

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Kudos [?]: 139576 [0], given: 12794

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P
Joined: 25 Feb 2013
Posts: 817

Kudos [?]: 381 [0], given: 42

Location: India
GPA: 3.82
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Runners V, W, X, Y, and Z are competing in the Bayville local triathlo [#permalink]

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New post 23 Dec 2017, 02:11
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Bunuel wrote:
Runners V, W, X, Y, and Z are competing in the Bayville local triathlon. If V finishes before W and W finishes before Z, how many ways can X finish before Y??

A. 5
B. 10
C. 30
D. 60
E. 120


No of ways 5 runners can run the race \(= 5!=120\)

Now order of finishing the race for V, W & Z is V...W...Z. VWZ among themselves can have \(3!=6\) positions but only \(1\) position is allowed.

So number of ways runners can run a race \(= \frac{120}{6}=20\)

Half the time X beats Y (and half the time Y beats X)

so no of ways X finishes before Y \(=\frac{20}{2} = 10\)

Option B

Kudos [?]: 381 [0], given: 42

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D
Joined: 02 Aug 2009
Posts: 5536

Kudos [?]: 6441 [1], given: 122

Runners V, W, X, Y, and Z are competing in the Bayville local triathlo [#permalink]

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New post 23 Dec 2017, 03:39
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Bunuel wrote:
Runners V, W, X, Y, and Z are competing in the Bayville local triathlon. If V finishes before W and W finishes before Z, how many ways can X finish before Y??

A. 5
B. 10
C. 30
D. 60
E. 120



Hi..

There are Two restrictions..
1) \(V>W>Z\)
2) \(X>Y\)

Let's just take first restriction...
1) \(V>W>Z\)
Total ways for all \(5 = 5!=120\)
V,W,Z can be arranged in 3! or 6 ways AND only one of it will be V>W>Z
So \(\frac{120}{6}=20\) ways..

2) now half of 20 will have x before y and half y before x..
So \(\frac{20}{2}=10\)
B...

niks18, you have missed out on first restriction and so you are getting D as answer above
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Kudos [?]: 6441 [1], given: 122

PS Forum Moderator
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P
Joined: 25 Feb 2013
Posts: 817

Kudos [?]: 381 [0], given: 42

Location: India
GPA: 3.82
GMAT ToolKit User Premium Member Reviews Badge CAT Tests
Re: Runners V, W, X, Y, and Z are competing in the Bayville local triathlo [#permalink]

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New post 23 Dec 2017, 03:49
chetan2u wrote:
Bunuel wrote:
Runners V, W, X, Y, and Z are competing in the Bayville local triathlon. If V finishes before W and W finishes before Z, how many ways can X finish before Y??

A. 5
B. 10
C. 30
D. 60
E. 120



Hi..

There are Two restrictions..
1) V>W>Z
2) X>Y

Let's just take first restriction...
1) V>W>Z
Total ways for all 5 = 5!=120
V,W,Z can be arranged in 3! or 6 ways AND only one of it will be V>W>Z
So 120/6=20 ways..
2) now half of 20 will have x before y and half y before x..
So 20/2=10
B...

niks18, you have missed out on first restriction and so you are getting D as answer above


Thanks chetan2u for highlighting :thumbup: . yup I completely ignored that condition :(

Kudos [?]: 381 [0], given: 42

Re: Runners V, W, X, Y, and Z are competing in the Bayville local triathlo   [#permalink] 23 Dec 2017, 03:49
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