4 variable Venn diagram, Please help me in solving below question

In Shishu Vidyalaya, students study at least one of 4 subjects from Hindi, English, Science or Maths. The

following additional information is known about the students in Shishu Vidyalaya

Subject(s) Number of Students

Hindi 54

English 77

Maths 91

Science 92

Further, it is also known that;

123 students study at least one of English and Science

The number of students who study Maths-English-Science is twice the number of students who

study Hindi-Maths.

The number of students who study Hindi-English, Hindi alone and Hindi-Science form an

arithmetic progression of common difference equal to 3.

The number of students who study Hindi-English-Science, All the four subjects, English alone and

Maths alone form an arithmetic progression of common difference equal to 2.

The number of students who study Maths alone is equal to the number of students who study

Maths-English, which is equal to the number of students who study Maths-English-Hindi.

The number of students who study Hindi-Maths is one more than the number of students who

study Maths alone.

The number of students who study Hindi-Science-Maths is equal to the 3

rd

prime number and

the number of students who study Maths-Science is equal to the 7

th

prime number.

1. What is the total number of students in Shishu Vidyalaya?

a. 150

b. 314

c. 160

d. 170

2. How many students study at least 2 of the 4 subjects?

a. 94

b. 96

c. 112

d. 111

3. If the number of students who study exactly 3 subjects is equal to 8K+1, what is the value of K?a. 4

b. 5

c. 6

d. 7

4. If 16 students who study English, 12 students who study Science and 14 students who study

Hindi leave the school, what could be the minimum number of students left in the school who

study Maths? –

a. 55

b. 60

c. 49

d. 57

Re: 4 variable Venn diagram, Please help me in solving below question

Hey Vishwa137.

Are you aware of probabilities and how they relate to Venn Diagrams?

In probability we can calculate P(A OR B) = P(A) + P(B) - P(A and B) and using this we get any statement of intersections and unions if we have enough information.

If you haven't come across this I can explain what it means but the idea is that you find the probabilities and then multiply it by the frequency to get the total number of people.