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05 Jul 2012, 16:15
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D
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Difficulty:
75%
(hard)
Question Stats:
54% (02:12) correct
46%
(02:19)
wrong
based on 507
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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
(A) Statement 1 alone is sufficient, but statement 2 alone is not.
(B) Statement 2 alone is sufficient, but statement 1 alone is not.
(C) Both statements together are sufficient, but neither alone is sufficient.
(D) Each statement alone is sufficient.
(E) Neither statement is sufficient, even when combined.
(1) 80 of the students study only German.
(2) 120 students study French or Spanish
(A) Statement 1 alone is sufficient, but statement 2 alone is not.
(B) Statement 2 alone is sufficient, but statement 1 alone is not.
(C) Both statements together are sufficient, but neither alone is sufficient.
(D) Each statement alone is sufficient.
(E) Neither statement is sufficient, even when combined.
31 Jan 2014, 05:51
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The key information in the question is none of the students who take French also take Spanish This means there is no overlap between French and Spanish at all. It also means 0 people take all the three languages and 0 people take Spanish and French together.
With this information, exactly two languages can only be {German+french} or {German+Spanish}
Stmt 1: 80 take only German. Given 100 take German. So 100-80 =20 take German+one other language Sufficient.
Stmt2: 120 taken French or spanish. That is {French}+{Spanish} = 120
We can use this formula:
{German}+{French}+{Spanish}-{Exactly two languages}-2*{all the three} = total
100+120-{Exactly two languages}-2*0=200
{Exactly two languages}=220-200 = 20.
Stmt2 is also Sufficient.
Hence D.
With this information, exactly two languages can only be {German+french} or {German+Spanish}
Stmt 1: 80 take only German. Given 100 take German. So 100-80 =20 take German+one other language Sufficient.
Stmt2: 120 taken French or spanish. That is {French}+{Spanish} = 120
We can use this formula:
{German}+{French}+{Spanish}-{Exactly two languages}-2*{all the three} = total
100+120-{Exactly two languages}-2*0=200
{Exactly two languages}=220-200 = 20.
Stmt2 is also Sufficient.
Hence D.
General Discussion
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.
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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