In a club, there are 58 members. Among them, 25 members drink tea, 23 members drink coffee and only 7 members drink both tea and coffee. What is the ratio of the number of members who drink tea or coffee but not both, to the number of members who drink neither tea nor coffee?
2 : 1
Let T = tea drinkers = 25, C = coffee drinkers = 23, both = 7.
Only tea = 25 − 7 = 18; only coffee = 23 − 7 = 16, so tea or coffee but not both = 18 + 16 = 34.
Tea or coffee (at least one) = 25 + 23 − 7 = 41, so neither tea nor coffee = 58 − 41 = 17.
Required ratio = 34 : 17 = 2 : 1.
Important Questions from Venn Diagram Problems
In a class of 75 students, 40 students participate in Cricket, 28 students participate in Hockey, and 12 students participate in both Cricket and Hockey, whereas 19 students do not participate in any of the two sports. How many students participate only in Hockey?
How many students like french?
A. 30
B. 35
C. 40
D. 45
What is the ratio of students who like Spanish to those who like German?
A. 2/3
B. 1/2
C. 3/2
D. 4/9
How many students like only one language?
A. 65
B. 70
C. 75
D. 85
L and A are classmates as well as good friends. In a class of 30 students, L has 10 unique friends and 5 friends who are common to A. A has a total of 17 friends in the class. How many students are friends with neither L nor A?
