Question

A survey of 135 freshmen business students at a local university produced the results listed below.

32 took English;
37 took math;
36 took religion;
16 took English but not math;
11 took math and religion;
12 took English and religion;
6 took all three

Question:


How many students took only religion (without math or English)?

(that's the green region)

Hint: Do NOT try to use a formula. Think your way through it.

And DRAW the Venn Diagram!

Answer 1

7 students took only religion .

We can solve this problem without using a formula.

We are given the following information:

Total students = 135

English only = 16

Math and religion = 11

English and religion = 12

All three = 6

We can calculate the number of students who took only religion by subtracting the number of students who took religion in combination with other subjects from the total number of students who took religion:

Students taking religion = 36

Students taking religion only = students_taking_religion - (math_and_religion + english_and_religion + all_three)

Students taking religion only = 36 - (11 + 12 + 6)

Students taking religion only = 7

Therefore, 7 students took only religion.