Directions for Questions 1 to 5: Refer to the data below and answer the questions that follow.
In a company of 500 employees, 250 play hockey, 225 play chess and 200 play badminton. 120 play both hockey and chess, 110 play both hockey and badminton and 70 play both chess and badminton and 50 play all the three.
1. How many employees play none of the games?
a) 50
b) 40
c) 65
d) 75
2. How many of them play only badminton?
a) 40
b) 45
c) 55
d) None of these
3. How many persons play neither hockey nor badminton?
a) 80
b) 85
c) 90
d) 75
Also Practice: MBA Logical Reasoning Questions & Answers – Venn Diagrams
4. How many play hockey alone?
a) 50
b) 60
c) 55
d) 70
5. How many players play hockey, chess and badminton alone?
a) 250
b) 230
c) 225
d) 220
Also Practice: Venn Diagrams – CAT Quantitative Aptitude
Directions for questions 6 and 7 : Study the figure given below and answer the questions.
6. In the figure given above, how many people are teachers, photographers and journalist but not politicians?
a) 3
b) 4
c) 6
d) 7
7. In the given figure how many people are politicians and journalist both?
a) 2
b) 5
c) 10
d) 12
Also Practice: Problems on Sets and Venn Diagrams
Directions for Questions 8 to 10: Refer to the data below and answer the questions that follow.
Last year, there were 3 sections CSAT mock Paper. Out of them 66 students cleared the cut-off in Section A, 68 students cleared the cut-off in Section B and 64 cleared the cut-off in Section C. 20 students cleared the cut-off in Section A and Section B, 18 cleared the cut-off in Section alone was equal and was 42 for each section.
8. How many cleared all the three sections?
a) 13
b) 12
c) 15
d) 17
9. How many cleared only one of the three sections?
a) 121
b) 163
c) 126
d) 152
10. The ratio of the numbers of students clearing the cut-off in one or more of the sections to the number of students clearing the cut off in Section A alone is?
a) 78/21
b) 3
c) 73/21
d) None of these
Answers:
Ques 1 |
Ques 2 |
Ques 3 |
Ques 4 |
Ques 5 |
Ques 6 |
Ques 7 |
Ques 8 |
Ques 9 |
Ques 10 |
---|---|---|---|---|---|---|---|---|---|
d |
d |
b |
d |
c |
d |
c |
b |
b |
a |
EXPLANATION
In this section we will explain the rationale for choosing the answer pertaining to every question. After practicing these MCQ(s), you would be able to understand the concepts of Venn Diagrams.
Explanation (1-5):
Given,
Total employees= 500
Number of employees playing hockey (a) = 250
Number of employees playing chess (b) = 225
Number of employees playing badminton (c) = 200
Number of employees playing hockey and chess (d) = 120
Number of employees playing hockey and badminton (e) = 110
Number of employees playing chess and badminton (f) = 70
Number of employees playing all the three (g) = 50
So we can deduce,
Number of employees playing hockey and chess alone (h) = Number of employees playing hockey and chess (d) - Number of employees playing all the three (g) = 120-50= 70
Similarly,
Number of employees playing hockey and badminton alone (i)= e-g= 110-50=60
Number of employees playing chess and badminton alone (j)= f-g= 70-50=20
Number of employees playing hockey alone= Number of employees playing hockey (a)-(Number of employees playing hockey and chess alone (h) + Number of employees playing hockey and badminton alone (i) + Number of employees playing all the three (g))
Number of employees playing hockey alone (k) = 250-(70+60+50) = 70
Similarly,
Number of employees playing chess alone (l) = 225-(70+20+50) = 85
Number of employees playing badminton alone (m) = 200-(20+60+50) = 70
This can be represented in Venn diagram as below:
1. Players playing none of the games= Total employees- Employees playing games
That is 500-(70+85+70+20+50+70+60) =75
2. Directly from Venn diagram, the answer is 70
3. Directly from Venn diagram, the answer is 85
4. Directly answer can be deduced from the Venn Diagram
5. Player playing all the games alone= k+l+m=70+85+70=225.
Explanation (6):
Clearly from the diagram there are 7 persons.
Explanation (7):
Common of politicians and Journalist = 2 + 3 + 5 = 10.
Detailed explanation (8 – 10):
Since, x = 12, the figure becomes:
Explanation (10)
(42 + 42 + 42 + 12 + 8 + 6 + 4)/42 = 78/21
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