At a certain school with 200 students, all children must

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At a certain school with 200 students, all children must [#permalink]

05 Jul 2012, 16:15

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At a certain school with 200 students, all children must take at least one of three language classes: German, French, and Spanish. If 100 students take German and none of the students who take French also take Spanish, then how many students take exactly two of the three language classes?

(1) 80 of the students study only German.
(2) 120 students study French or Spanish

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Re: At a certain school with 200 students, all children must [#permalink]

06 Jul 2012, 15:02

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Refer to the pic: G=students taking German; F= students taking French; S= students taking Spanish

According to the problem:
total = 200 students
G=100
students outside G,F,S = 0
F and S have no intersection (as drawn on the pic) -> there are no students taking all 3 classes.

1) 80 students are only G -> G = (only G) + GF + GS, the intersections GF + GS = 20. Sufficient.

2) F + S = 120 (they have no intersection) -> Total = G + F + S - (GF + GS) (compensating for double counting). Everything in that equation is given except the intersections GF+GS which can be determined. Sufficient.

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Re: At a certain school with 200 students, all children must [#permalink]

17 Sep 2012, 13:10

Bunuel

can you please help vvith this problem

Thanks

Re: At a certain school with 200 students, all children must [#permalink] 17 Sep 2012, 13:10

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At a certain school with 200 students, all children must

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At a certain school with 200 students, all children must

At a certain school with 200 students, all children must

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