Sets and Venn diagrams

2011 · Q42

There are 100 students in a particular class. 60% students play cricket, 30% student play football and 10% students play both the games. What is the number of students who play neither cricket nor football?

1. (a)25
2. (b)20UPSC key
3. (c)18
4. (d)15

2012 · Q48

In the above figure, circle P represents hardworking people, circle Q represents intelligent people, circle R represents truthful people, and circle S represents honest people. Which region represents the people who are intelligent, honest and truthful but not hardworking?

1. (a)6UPSC key
2. (b)7
3. (c)8
4. (d)11

2013 · Q63

Out of 120 applications for a post, 70 are male and 80 have a driver’s license. What is the ratio between the minimum to maximum number of males having driver’s license?

1. (a)1 to 2
2. (b)2 to 3
3. (c)3 to 7UPSC key
4. (d)5 to 7

2014 · Q19

There are 50 students admitted to a nursery class. Some students can speak only English and some can speak only Hindi. 10 students can speak both English and Hindi. If the number of students who can speak English is 21, then how many students can speak Hindi, how many can speak only Hindi and how many can speak only English?

1. (a)21, 11 and 29 respectively
2. (b)28, 18 and 22 respectively
3. (c)37, 27 and 13 respectively
4. (d)39, 29 and 11 respectivelyUPSC key

2014 · Q24

Out of a total of 120 musicians in a club, 5% can play all the three instruments, guitar, violin and flute. It so happens that the number of musicians who can play any two and only two of the above instruments is 30. The number of musicians who can play the guitar alone is 40. What is the total number of those who can play violin alone or flute alone?

1. (a)45
2. (b)44UPSC key
3. (c)38
4. (d)30

2015 · Q31

In a town, 45% population read magazine A, 55% read magazine B, 40% read magazine C, 30% read magazines A and B, 15% read magazines B and C, 25% read magazines A and C; and 10% read all the three magazines. What percentage do not read any magazine?

1. (a)10%
2. (b)15%
3. (c)20%UPSC key
4. (d)25%

2015 · Q36

Out of 130 students appearing in an examination, 62 failed in English, 52 failed in Mathematics, whereas 24 failed in both English and Mathematics. The number of students who passed finally is

1. (a)40UPSC key
2. (b)50
3. (c)55
4. (d)60

2015 · Q37

In a group of persons travelling in a bus, 6 persons can speak Tamil, 15 can speak Hindi and 6 can speak Gujarati. In that group none can speak any other language. If 2 persons in the group can speak two languages only and one person can speak all the three languages, then how many persons are there in the group?

1. (a)21
2. (b)22
3. (c)23UPSC key
4. (d)24

2015 · Q51

The number of persons who read magazine X only is thrice the number of persons who read magazine Y. The number of persons who read magazine Y only is thrice the number of persons who read magazine X. Then, which of the following conclusions can be drawn?

1.The number of persons who read both the magazines is twice the number of persons who read only magazine X.

2.The total number of persons who read either one magazine or both the magazines is twice the number of persons who read both the magazines.

Select the correct answer using the code given below:

1. (a)1 only
2. (b)2 only
3. (c)Both 1 and 2
4. (d)Neither 1 nor 2

2018 · Q42

19 boys turn out for playing hockey. Of these, 11 are wearing hockey shirts and 14 are wearing hockey pants. There are no boys without shirts and/or pants. What is the number of boys wearing full uniform?

1. (a)3
2. (b)5
3. (c)6UPSC key
4. (d)8

2019 · Q20

In a conference, out of a total 100 participants, 70 are Indians. If 60 of the total participants are vegetarian, then which of the following statements is/are correct?

1.At least 30 Indian participants are vegetarian.

2.At least 10 Indian participants are non-vegetarian.

Select the correct answer using the codes given below:

1. (a)1 only
2. (b)2 only
3. (c)Both 1 and 2UPSC key
4. (d)Neither 1 nor 2

2019 · Q31

All members of a club went to Mumbai and stayed in a hotel. On the first day, 80% went for shopping and 50% went for sightseeing, whereas 10% took rest in the hotel. Which of the following conclusion(s) can be drawn from the above data?

1.40% members went for shopping as well as sightseeing.

2.20% members went for only shopping.

Select the correct answer using the code given below:

1. (a)1 onlyUPSC key
2. (b)2 only
3. (c)Both 1 and 2
4. (d)Neither 1 nor 2

2019 · Q52

In a group of 15 people; 7 can read French, 8 can read English while 3 of them can read neither of these two languages. The number of people who can read exactly one language is

1. (a)10
2. (b)9UPSC key
3. (c)5
4. (d)4

2021 · Q35

In a group of 120 persons, 80 are Indians and rest are foreigners. Further, 70 persons in the group can speak English. The number of Indians who can speak English is

1. (a)20
2. (b)30
3. (c)30 or less
4. (d)30 or moreUPSC key

2021 · Q46

Half of the villagers of a certain village have their own houses. One-fifth of the villagers cultivate paddy. One-third of the villagers are literate. Four-fifth of the villagers are under 25 years of age. Which one of the following statements is certainly correct?

1. (a)All the villagers who have their own houses are literate.
2. (b)Some villagers under 25 years of age are literate.UPSC key
3. (c)Only half of the villagers who cultivate paddy are literate.
4. (d)No villager under 25 years of age has his own house.

2024 · Q28

In an examination, 80% of students passed in English, 70% of students passed in Hindi and 15% failed in both the subjects. What is the percentage of students who failed in only one subject?

1. (a)15%
2. (b)20%UPSC key
3. (c)25%
4. (d)35%