In a survey of 100 students, the number s studying various languages were found to be: Spanish, 28; German, 30; French, 42; Spanish and German, 8; Spanish and French, 10; German and French, 5; all three languages, 3.

Question

(a)How many students were studying no language?
(b)How many students had French as their only language?
(c)How many students studied German if and only if they studied French?

Answer 1

a) add up all the students, then subtract from 100:
100-(28+30+42)=0
You don't need to account for the students taking multiple classes because they will already be counted in the individual class.

b) subtract the number of people taking french and another class from the total number of french students:
42-(10+5)=27

c) the number of students who took both french and German:
5

Answer 2

In a survey of 100 students, the numbers studying various languages were found to be: Spanish 28: German 30: French 42: Spanish and French 10: Spanish and German 8: German and French 5: all the three languages 3. How many students were studying no language?

Answer 3

very satisfaction !