Question

The Venn diagram above represents the students who were sick one day in January at a Chicago high school. 80 students had only a fever, 60 students had only a cough, 90 students had only a headache, 10 students had only a cough and fever, 30 students had only a cough and a headache, 40 students had only a fever and a headache, and 20 students had a fever, cough, and headache. 100 students had other reasons for being absent that day. None of the sick students attended school that day. If 800 students attend the high school, how many students were at school that day?

Answer 1

370

Explanation:

The venn diagram corresponds to students who were sick in January at a Chicago high school.

Students who had only fever= n(A) = 80

Students who had only headache= n(B) = 90

Students who had only cough = n(C) =60

Students who had both cough and fever = n(AC) = 10

n(AB) = 40:n(BC) = 30 n(ABC) = 20

Hence total students = 800

no of students who were absent due to other reasons = 100

REmaining students = 700

Students who were sick = sum of all =330

So no of students who were at school = 700-330 = 370