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At a certain school with 200 students

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At a certain school with 200 students

by gmatdriller » Sat Aug 13, 2011 11:42 pm
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

OA D
Please your explanations should dwell more on (2).
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Source: — Data Sufficiency |
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by GMATGuruNY » Sun Aug 14, 2011 3:42 am
gmatdriller wrote: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

OA D
Please your explanations should dwell more on (2).
Let B = number who take 2 languages.

Total = only G + only F + only S + B.

Image

Everything in the G circle = 100.
Thus, everything outside the G circle = 100.
Thus, only F + only S = 100.
Thus:
200 = only G + 100 + B
B = 100 - only G.

Question: What is B?

Statement 1: 80 of the students study only German.
B = 100-80 = 20.
Sufficient.

Statement 2: 120 students study F or S.
only F + only S + B = 120.
Since only F + only S = 100, B = 20.
Sufficient.

The correct answer is D.
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by gmatdriller » Sun Aug 14, 2011 3:01 pm
your explanations make sense. I appreciate
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