In a certain class, 1/3 of the students are honors students, : PS Archive
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In a certain class, 1/3 of the students are honors students,

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In a certain class, 1/3 of the students are honors students, [#permalink]

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15 Jun 2008, 14:34
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In a certain class, 1/3 of the students are honors students, and 1/4 of the students play varsity sports. If 12 students play varsity sports and are honors students, what is the least possible number of students in the class?
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Re: PS - In a certain class [#permalink]

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15 Jun 2008, 14:49
Agree with 48.

Here is the solution.

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In a certain class, 1/3 of the students are honors students, and 1/4 of the students play varsity sports. If 12 students play varsity sports and are honors students, what is the least possible number of students in the class?

Let n be the number of students in the class. The least possible n corresponds to the situation when 12 students is as large part of the class as possible. This occurs when all those who play varcity sports are also honors students – and in this case, 12=1/4*n and n=48. Now, we need to check if 1/3 and 1/4 of n are integer numbers – yes, they are; so n=48 is the answer.
Re: PS - In a certain class   [#permalink] 15 Jun 2008, 14:49
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