Question 23

In a survey of 100 students, the number of students studying various languages were found to be:
1. English only-18
2. English but not Hindi-23
3. English and German-8
4. English-26
5. German-48
6. German and Hindi-8
7. No language-24
Then, which of the following statements are true?
A. Number of students who were studying Hindi is 18.
B. Number of students who were studying English and Hindi is 3.
C. Number of students who were studying English, Hindi and German is 3.

Solution

Only English = 18

English but not Hindi = 23. This implies that students studying English and German but not Hindi will be = 23 - 18 = 5.

English and German = 8. Now, students studying English and German but not Hindi = 5, thus students studying all three will be = 8 - 5 = 3

English = 26, and students studying English and German = 8 and only English = 18; thus students studying English and Hindi but not german = 26 - 18 - 8 = 0

German and Hindi = 8. Students studying all three languages = 3, thus students studying German and Hindi, but not English = 8 - 3 = 5.

German = 48. Thus, students studying only German will be = 48 - 5 - 3 - 5 = 35

No language = 24.

Total number of students = 100

Number of students studying only Hindi = 100 - (18 + 5 + 35 + 3 + 5 + 10 + 24) = 10

A. Number of students who were studying Hindi = 18. TRUE
B. Number of students who were studying English and Hindi = 3. TRUE
C. Number of students who were studying English, Hindi and German = 3. TRUE

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