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# In my class, everyone plays at least one sport. There are 99

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Joined: 04 Jan 2006
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In my class, everyone plays at least one sport. There are 99 [#permalink]  10 Feb 2007, 11:40
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In my class, everyone plays at least one sport. There are 99 students other than me. 50 of us play soccer, 45 basketball and 50 play volleyball. Only 15 of us play all three games. Everyone plays at least one game. How many play only two games?

A. 10
B. 15
C. 20
D. 25
E. 30
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Re: PS: Set and Word Problem [#permalink]  10 Feb 2007, 13:01
devilmirror wrote:
In my class, everyone plays at least one sport. There are 99 students other than me. 50 of us play soccer, 45 basketball and 50 play volleyball. Only 15 of us play all three games. Everyone plays at least one game. How many play only two games?

A. 10
B. 15
C. 20
D. 25
E. 30

Getting 15

Using Venn Diagrams

A - Only Soccer = 50 - (x+y+15)
B - Only Basketball = 45 - (x+z+15)
C - Only VolleyBall = 50 -(y + z+15)

Only AB+ Only BC+ Only CA = x+y+z

We know ABC =15

Total = Only A + Only B + Only C + Only AB+ Only BC+ Only CA + ABC + None
Re: PS: Set and Word Problem   [#permalink] 10 Feb 2007, 13:01
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