GRE Venn diagram type of question

5. In a class of 78 students 41 are taking French, 22 are taking German. Of the students taking French or German, 9 are taking both courses. How many students are not enrolled in either course?
A. 6
B. 15
C. 24
D. 33
E. 54

I havent done statistics in so long. When I read this i read that of the 63 taking a foreign language 9 were taking both and didnt really contribute to the 63 total...like it was superfluous info. I was wrong. anyone able to tell me more accurately what the question was actually saying?

You titled this "Venn diagram". Did you actually draw a Venn diagram for the problem?

Draw two overlapping circles, one representing the students taking French, the other representing the students taking German. The overlapping part is students taking both. So what number should you write there? There are 41 students taking French. So what number of those students are not also taking German? Write that number in the portion of the "French" circle that is not overlapping the "German" circle. There are 22 students taking German. So what number of those students are not also taking French? Write that number in the portion of the "German" circle that is not overlapping the "French" circle.

How many students are taking French or German or both? (It is NOT 63!)

ash9231 said:

I havent done statistics in so long.

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To refresh on this topic, please try online lessons such as this one.

ash9231 said:

When I read this i read that of the 63 taking a foreign language 9 were taking both and didnt really contribute to the 63 total.

Click to expand...

I don't follow your reasoning...? This exercise is asking you about the numbers of students taking either of two classes. Why would they want you to ignore some of those students?

ash9231 said:

5. In a class of 78 students 41 are taking French, 22 are taking German. Of the students taking French or German, 9 are taking both courses. How many students are not enrolled in either course?

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Draw the diagram (being two overlapping circles inside a rectangle). The "universe" is 78, so label the rectangle with this value. Label one of the circles as "German" with a value of 22; label the other as "French" with a value of 41.

You are told that nine of the students were taking both French and German. Put this value in the overlapping portion of the diagram.

Given that 41 -- total -- are taking French and that 9 of these are also taking German, how many are only taking French? (Hint: Subtract.) Put this value in the non-overlapping portion of the "French" circle. Do the same kind of computation for the "German" circle.

You now have a diagram showing the students studying French, German, or both. How many students are in the circles? (Hint: Add the three sections.) You also know that the entire class (that is, your "universe") is 78. So how many students are inside the rectangle but outside the circles? (Hint: Subtract.)