Q1. How many numbers are there between 1 and 100 that are not divisible by 2, 3 and 5 ?
A. 21
B. 22
C. 20
D. 24
E. None of these
Answer - Option D
Explanation -
We can solve this question by drawing a Venn diagram.
From the above diagram it is clear that (27 + 14 +7 + 7 + 13 + 3 + 3 = 76 ) 76 numbers are divisible by either 2,3 or 5.
So 100 - 76 = 24 numbers are not divisible by 2,3 or 5.
Q2. In a class,7 students like to play Basketball and 8 like to play Cricket. 3 students like to play on both Basketball and Cricket. How many students like to play Basketball or Cricket or both?
A. 10
B. 9
C. 12
D. 11
E. None of these
Answer - Option C
Explanation -
Draw a Venn Diagram yourself !
B + C - BC = Number of students that play either Basketball or Cricket
7 +8 - 3 = 12
Directions (Q3 - Q4): A college has 63 students studying Political Science, Chemistry and Botany. 33 students study Political Science, 25 Chemistry and 26 Botany. 10 study Political Science and Chemistry, 9 study Botany and Chemistry while 8 study both Political Science and Botany. Same number of students study all three subjects as those who learn none of the three.
Q3. How many students study all the three subjects?
A. 2
B. 3
C. 5
D. 7
E. None of these
Answer - Option B
Explanation -
From the above diagram you can clearly see that 3 students study all three subjects.
Q4. How many students study only one of the three subjects?
A. 21
B. 30
C. 39
D. 42
E. None of these
Answer - Option C
Explanation -
Number of students who study only one subject = 18 + 9 +12 = 39
Q5. In a college, 200 students are randomly selected. 140 like tea, 120 like coffee and 80 like both tea and coffee.
- How many students like only tea?
- How many students like only coffee?
- How many students like neither tea nor coffee?
- How many students like only one of tea or coffee?
- How many students like at least one of the beverages?
A. 150
B. 160
C. 170
D. 180
E. None of these
Answer - Option D
Explanation -
The given information may be represented by the following Venn diagram, where T = tea and C = coffee.
Number of students who like only tea = 60
Number of students who like only coffee = 40
Number of students who like neither tea nor coffee = 20
Number of students who like only one of tea or coffee = 60 + 40 = 100
Number of students who like at least one of tea or coffee = n (only Tea) + n (only coffee) + n (both Tea & coffee) = 60 + 40 + 80 = 180