At a certain school with 200 students, all children must

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

Thus both the statements give same information and are sufficient.

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:

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