Question

254 students study english

280 students study math
280 students study science
73 students study all topics
152 students study english and math
79 students study math and science
139 students study science and english
How much students are in the school?​

Answer 1

517

Explanation:

We can draw a Venn diagram to represent the data.

First, identify the groups.

• Let E = students who study English
• Let M = students who study Math
• Let S = students who study Science

Then draw the Venn diagram to represent the groups.

Given 73 students study all subjects:

E ∩ M ∩ S = 73 (add this to the middle section)

Next, add the numbers for the sections where the students study 2 topics.

E ∩ M but not S: 152 - 73 = 79

M ∩ S but not E: 79 - 73 = 6

S ∩ E but not M: 139 - 73 = 66

Now complete each circle by making sure that the values add up to the total value given.

Only E = 254 - S ∩ E - E ∩ M - E ∩ M ∩ S = 254 - 66 - 79 - 73 = 36

Only M = 280 - E ∩ M - M ∩ S - E ∩ M ∩ S = 280 - 79 - 6 - 73 = 122

Only S = 280 - M ∩ S - S ∩ E - E ∩ M ∩ S = 280 - 6 - 66 - 73 = 135

To find the total number of students in the school, add the numbers in each section of the Venn diagram:

73 + 79 + 6 + 66 + 36 + 122 + 135 = 517