Question: 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 the courses. How many students are not enrolled in either course?

1. 6
2. 15
3. 24
4. 33
5. 54

“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 the courses. How many students are not enrolled in either course?”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book “GMAT Official Guide Quantitative Review”. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. The GMAT Quant topic in the problem-solving part requires calculative mathematical problems that should be solved with proper mathematical knowledge.

Solution and Explanation

Approach Solution 1:

Formula for calculating two overlapping sets:
A + B – both + NOT (A or B) = Total
So in our task we have equation:
41 (French) + 22 (German) – 9(both) + NOT = 78
54 + NOT = 78
NOT = 78 – 54 = 24

Correct Answer: C

Approach Solution 2:

We are given:
Total = 78
French total = 41
French and German = 9
So, French total – French and German = 41 – 9 = 32
German total: 22
French and German: 9
So, German total – French and German = 22 – 9 = 13

Finally, 78 – 9 – 13 – 32 = 24

Correct Answer: C

Approach Solution 3:

You could solve this by drawing a Venn diagram. A simpler way is to realize that you can subtract the number taking both languages from the numbers taking French to find the number taking only French. Likewise find those taking only German. Then we have :

Total = only French + only German + both + neither

Therefore, Not enrolled students = 24

Correct Answer: C

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