Three-set Venn Diagram Problem

vishugogo wrote:At a certain school with 200 students, all children must take at least one of the three languages 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

I wouldn't use a Venn diagram here.
None of the students who take French also take Spanish.
Implication: no student studies all 3 languages.

Statement 1: 80 students study only German
TOTAL German = 100.
ONLY German = 80.
Thus, the number of students who study German AND another language = 100-80 = 20.
SUFFICIENT.

Statement 2: 120 students study French or Spanish
Implication: the remaining 80 students study ONLY GERMAN.
Same information as that given in statement 1.
SUFFICIENT.

The correct answer is D.

GMATGuruNY wrote:

vishugogo wrote:At a certain school with 200 students, all children must take at least one of the three languages 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

I wouldn't use a Venn diagram here.
None of the students who take French also take Spanish.
Implication: no student studies all 3 languages.

Statement 1: 80 students study only German
TOTAL German = 100.
ONLY German = 80.
Thus, the number of students who study German AND another language = 100-80 = 20.
SUFFICIENT.

Statement 2: 120 students study French or Spanish
Implication: the remaining 80 students study ONLY GERMAN.
Same information as that given in statement 1.
SUFFICIENT.

The correct answer is D.

Hi Mitch,
The question is little bit vague to me.
1) I could not understand the statement "None of the students who take French also take Spanish". How does it mean ->"no student studies all 3 languages."

2) Are they asking us to find GF+GS+FS = ?

Could you please explain this in an generous manner.

Thanks in advance.

Regards,
Uva.

Uva@90 wrote:

GMATGuruNY wrote:

vishugogo wrote:At a certain school with 200 students, all children must take at least one of the three languages 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

I wouldn't use a Venn diagram here.
None of the students who take French also take Spanish.
Implication: no student studies all 3 languages.

Statement 1: 80 students study only German
TOTAL German = 100.
ONLY German = 80.
Thus, the number of students who study German AND another language = 100-80 = 20.
SUFFICIENT.

Statement 2: 120 students study French or Spanish
Implication: the remaining 80 students study ONLY GERMAN.
Same information as that given in statement 1.
SUFFICIENT.

The correct answer is D.

Hi Mitch,
The question is little bit vague to me.
1) I could not understand the statement "None of the students who take French also take Spanish". How does it mean ->"no student studies all 3 languages."

2) Are they asking us to find GF+GS+FS = ?

Could you please explain this in an generous manner.

Thanks in advance.

Regards,
Uva.

In a school that offers German, French and Spanish, the following overlaps are possible:
GF + GS + FS + GFS.
In this particular school, no student who takes French also takes Spanish.
Thus, none of the red pairings above are allowed, leaving the following possible overlaps:
GF + GS.

Since the question stem asks for the number of students who study exactly 2 languages, we need to know the value of GF + GS.
Since 100 students in total study German, we get:
100 = Only German + GF + GS.
Thus, to determine the value of GF + GS, we need to know the value of Only German.

Question rephrased: How many students study Only German?

As shown in my post above, each statement on its own indicates that Only German = 80.
Thus, each statement on its own is SUFFICIENT.

GMATGuruNY wrote:

Uva@90 wrote:

GMATGuruNY wrote:

vishugogo wrote:At a certain school with 200 students, all children must take at least one of the three languages 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

I wouldn't use a Venn diagram here.
None of the students who take French also take Spanish.
Implication: no student studies all 3 languages.

Statement 1: 80 students study only German
TOTAL German = 100.
ONLY German = 80.
Thus, the number of students who study German AND another language = 100-80 = 20.
SUFFICIENT.

Statement 2: 120 students study French or Spanish
Implication: the remaining 80 students study ONLY GERMAN.
Same information as that given in statement 1.
SUFFICIENT.

The correct answer is D.

Hi Mitch,
The question is little bit vague to me.
1) I could not understand the statement "None of the students who take French also take Spanish". How does it mean ->"no student studies all 3 languages."

2) Are they asking us to find GF+GS+FS = ?

Could you please explain this in an generous manner.

Thanks in advance.

Regards,
Uva.

In a school that offers German, French and Spanish, the following overlaps are possible:
GF + GS + FS + GFS.
In this particular school, no student who takes French also takes Spanish.
Thus, none of the red pairings above are allowed, leaving the following possible overlaps:
GF + GS.

Since the question stem asks for the number of students who study exactly 2 languages, we need to know the value of GF + GS.
Since 100 students in total study German, we get:
100 = Only German + GF + GS.
Thus, to determine the value of GF + GS, we need to know the value of Only German.

Question rephrased: How many students study Only German?

As shown in my post above, each statement on its own indicates that Only German = 80.
Thus, each statement on its own is SUFFICIENT.

Mitch,
Thanks for your great explanation. I got it.