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# a class has 1/3 in football and 1/4 of students in basket

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Director
Joined: 07 Jun 2004
Posts: 612
Location: PA
a class has 1/3 in football and 1/4 of students in basket [#permalink]

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23 Jan 2005, 12:33
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a class has 1/3 in football and 1/4 of students in basket ball. And 12 play both. What is the least possible number fo students in th class

20

22

36

48

144

VP
Joined: 18 Nov 2004
Posts: 1433

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23 Jan 2005, 13:05
48.

All basketball players also play football....12 players.....and 4 football players only play football and we already have a common pool of 12 players.

Backsolving helps.....selection 1 and 2 r out as they r not divisible by 3 and 4...36 doesn't yield the result....as 1/4*36 = 9 basketball players...however, we already know that there r atleast 12 basketball players (the common one)....48 is the least that satisfies everything.

Football = 16

Total basket +baseball = 16
Students who do not play anything is = 48-16 = 32
Director
Joined: 07 Jun 2004
Posts: 612
Location: PA

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23 Jan 2005, 17:08
thanks now iget it i was wondering why it was not 36
VP
Joined: 25 Nov 2004
Posts: 1483

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23 Jan 2005, 19:31
rxs0005 wrote:
thanks now iget it i was wondering why it was not 36

Yes, it is 48 and not 36. if 36 were the total number of students, then the number of students who play would be negative which is not possible. if 48 were the total number of students, the number of students who play basketball would be 12 and all basketbal players play footvball too.
SVP
Joined: 03 Jan 2005
Posts: 2233

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24 Jan 2005, 00:39
Both 1/3N and 1/4N must be greater than 12. So N=48.
24 Jan 2005, 00:39
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# a class has 1/3 in football and 1/4 of students in basket

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