Ch.17 :- Arithmetical Reasoning : Exercise 1


1. There are 50 students admitted to a nursery class. Some students can speak only English and some can speak only Hindi. Ten 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, only Hindi and only English.
(a) 39,29 and 11, respectively
(b) 37, 27 and 13, respectively
(c) 28, 18 and 22, respectively
(d) 21, 11 and 29, respectively

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2. Consider the Venn diagram given below:

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The numbers in Venn diagram indicates the number of persons reading the newspapers. The diagram is drawn after surveying 50 persons. In a population of 10,000, how many can be expected to read at least two newspapers?
(a) 5,000
(b) 5,400
(c) 6,000
(d) 6,250

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3. 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 and one person can speak all the three languages, then how many persons are there in the group?
(a) 21
(b) 22
(c) 23
(d) 24

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4. 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?
(a) 30
(b) 38
(c) 44
(d) 45

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✦Directions for Q. No.5 to 7 : Head the following information carefully and then answer the question that follow:
A publishing firm publishes newspapers A, B and C. In an effort to persuade advertisers to insert advertisements in these newspapers, the firm sends out the following statements to possible advertisers:

A survey of representative sample of the whole population shows that-

Newspaper A is read by 26%.
Newspaper B is read by 25%.
Newspaper C is read by 14%.
Newspaper A and B are read by 11%.
Newspaper B and C are read by 10%.
Newspaper C and A are read by 9%.
Newspaper C only is read by 0%.

5. The percentage of readers who read ail the three newspapers is
(a) 1
(b) 4
(c) 5
(d) 6

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6. The percentage of readers who read Newspapers A and B but not C, is
(a) 2
(b) 4
(c) 5
(d) 6

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7. The percentage of readers who read at least one of the three newspapers is
(a) 40
(b) 50
(c) 60
(d) 65

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✦Directions for Q. No.8 to 10: The following diagram shows the number of students who got distinction in three subjects in a total of 500 students. Study the diagram carefully and then answer the questions that follow:

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8. What is the percentage of students who got distinction in two subjects?
(a) 8%
(b) 9%
(c) 10%
(d) 12%

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9. What is the percentage of students who got distinction?
(a) 28%
(b) 18.6%
(c) 38%
(d) 15%

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10. The percentage of students with distinction marks in mathematics is :
(a) 17.8%
(b) 18.6%
(c) 19.2%
(d) 20.6%

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✦Directions for Q. No. 11 to 13 : These questions are based on the following information for an examination:
(A) Candidates appeared 10500
(B) Passed in all the five subjects 5685
(C) Passed in three subjects only 1498
(D) Passed in two subjects only 1250
(E) Passed In one subject only 835
(F) Failed in English only 78
(G) Failed in Mathematics only 275
(H) Failed in Physics only 149
(I) Failed in Chemistry only 147
(J) Failed in Biology only 221

11. How many candidates failed in ail the subjects?
(a) 4815
(b) 3317
(c) 2867
(d) 362

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12. How many candidates passed in at least four subjects?
(a) 6555
(b) 5685
(c) 1705
(d) 870

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13. How many candidates failed because of having failed in four or less subjects?
(a) 4815
(b) 4453
(c) 3618
(d) 2368

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✦Directions for Q. No. 14 to 18 : These questions are based on the information given below:
Data of 450 candidates, who took part in an examination in social sciences, Mathematics and Science is given as below:
(A) Passed in all the subjects 167
(B) Failed in all the subjects 60
(C) Failed in Social sciences 175
(D) Failed in Mathematics 199
(E) Failed in Science 191
(F) Passed in Social sciences only 62
(G) Passed in Mathematics only 481
(H) Passed in Science only 52

14 How many candidates failed in Social science only?
(a) 15
(b) 21
(c) 30
(d) 42

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15. How many candidates failed in one subject only?
(a) 152
(b) 144
(c) 61
(d) 56

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16. How many candidates passed in Mathematics and at least in one more subject?
(a) 210
(b) 203
(c) 170
(d) 94

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17. How many candidates failed in two subjects only?
(a) 56
(b) 61
(c) 152
(d) 162

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18. How many candidates passed in at least one subject?
(a) 450
(b) 390
(c) 304
(d) 167

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19. Five years ago Vinay’s age was one-third of the age of Vikas and now Vinay’s age is 17 years. What is the present age of Vikas ?
(a) 9 years
(c) 41 years
(b) 36 years
(d) 51 years

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20. Pushpa is twice as old as Rita was two years ago. If difference between their ages be 2 years, how old is Pushpa today?
(a) 6 years
(b) 8 years
(c) 10 years
(d) 12 years

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21. 10 years ago, Chandravati’s mother was 4 times older than her daughter. After 10 years, the mother will be twice older than the daughter. The present age of Chandravati is :
(a) 5 years
(c) 20 years
(b) 10 years
(d) 30 years

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22. The sum of ages of a father and son is 45 years. Five years ago the product of their ages was 4 times the father’s age at that time. The present age of the father and son, respectively are:
(a) 25 years, 10 years
(b) 36 years, 9 years
(c) 39 years, 6 years
(d) none of these

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