At a certain school with 200 students, all children must

Question

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

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

gmatprav · Accepted Answer

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.

tutorphd · Answer

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.

jlgdr · Answer

I would just use two simple venn diagrams for this problem. Let's proceed

Statement 1 tells us that German only is 80. Therefore, since we know that non of the students speak 3 languages or both french and spanish we can infer that German+French and German+Spanish = 20 students. Thus, we have a total of 20 students that speak exactly two languages.

Sufficient

Statement 2, we would have the same diagram knowing that Spanish of French only represent 120 total. Therefore, since we know the grand total is 200 if we add all German + (Spanish or French) we get 220. Now, since our total is 200 and none of them speaks 3 languages them we have that exactly 2 must be equal to 20.

Sufficient

D

Nevernevergiveup · Answer

VennDiagram_900.gif New Doc.jpg Thus both the statements give same information and are sufficient.

Bunuel · Answer

Veritas Prep Official Explanation To deal with this type of three-set Venn Diagram problem, first create a diagram that inserts all the information given in the question stem itself. The obvious information given is the fact that there are 200 total students, of which 100 take German. Also given is the fact that there are no students taking French and Spanish together. Less obvious is the fact that there are no students taking neither of the classes (“all students must take at least one”), and there are no students taking all three languages. (If there are no students taking both French and Spanish, then there cannot be any students taking all three.) Once this is mapped out (which is the hardest part of the problem and is shown below), it is clear that statement (1) is sufficient, because if 80 take only German, then there must be 20 students total who take only German and Spanish or only German and French. Since the question wants exactly that total, then the answer is 20, and statement (1) is sufficient. In statement (2), you learn that the total value of the French and Spanish circles is 120. Since you know that there are 200 total students and 100 students who take German, the overlap between the sets must be 20 (200 = 100 + 120 – overlap ), and this is also sufficient to answer the question. The correct answer choice is D. Below is the information given in the question stem. This allows you to see how plugging in each statement in will allow you to solve for the sum of exactly two regions: 2021-01-13_13-24-44.png

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At a certain school with 200 students, all children must

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