Exercise Problems and solution (Counting & Venn diagram)

Question: 1 All the 120 students of 12th batch BBA program are members of the IT club or the debate club or both. If 90 Students enrolled in the IT club and 70 students enrolled in the debate club, how many students are in both the clubs?
 (a) 25 (b) 30 (c) 35 (d) 40

Question: 2 All 120 students in a class play cricket or football or both, 75 play cricket and 60 play football. How many students play both?
(a) 15 (b) 25 (c) 13 (d) 20


 Question: 3 In a survey of group of people, it was found that 50% had iodine deficiency, 25% had diabetes and 12% had both. What percentage to people in that group had none of these two ailments?
(a) 63% (b) 37% (c) 25% (d) 13%


Question: 4 In a survey of group of people, it was found that 60% had iodine deficiency, 30% had debates & 16% had both. What % of people in  the group had none of these two ailments?
(a) 26% (b) 24% (c) 25% (d) 30% (e) None

Question: 5 In an examination 52% students failed in English, 42% failed in Mathematics. If 17% failed in both subjects, find the percentage of students who passed in both subjects.
(a) 23 (b) 20 (c) 18 (d) 25 (e)22

Question: 6 In a class of 120 students, 60% can speak French and the rest can speak only English. If 25% of those in the class who can speak French can also speak English, how many of the students in the class can speak English?
 (a) 54 (b) 60 (c) 60 (d) 84

Question: 7 In a party attended by 32 people, 24 were students. If 12 of those in attendance were women & 6 of the women in attendance were students, how many of the men who attended the party were not students?
(a) 2 (b) 3 (c) 4 (d) 5 (e) 6


Question: 8 Of the 65 cars on a car lot, 45 have air conditioning, 30 have power windows and 12 have both air conditioning and power windows. How many cars on the lot have neither air conditioning nor power windows?
(a) 5 (b) 10 (c) 4 (d) 2 (e) None


Question: 9 In a city 90% of the population own a car, 15% own a motor cycle, and everybody owns one or the other or both. What is the percentage of motorcycle owners who own car?
(a) 5% (b) 15% (c) 33(1/3)% (d) 50% (e)  90%




Exercise Solutions 
1. (D)

:. 90-X+X+70-X= 120
=> 160-X = 120
=> X = 160-120 =40

2. (A)

:. 75-X+X+60-X=120
=> 135-X= 120
=>X=135-120=15

3.(B)
100%-{(50%-12%)+(25%-12%)+12%}= 37%

4. (E)

24+16+44+X=100
=> 84+X=100
:. X=16%

5.(A)
Total percentage of students who failed in 1 or 2 subjects
= 52+42-17=94-17
=77%
:. Students who did not fail in any subject is (100-77)= 23%
:. Students who passed in all subjects is 23%

6.(C)

French can speak by 120x60% = 72 Students
Only English can speak by 120-72= 48 Students
Both French & English can speak by 72 x 25%=18 Students


English can speak by 48+18 = 66 Students

7. (A)

:. X+18+6+6=32
=>X+30=32
=>X=2


8. (D)

:. X+33+12+18=65
=> X=65-63=2

9. (A)

:. 90-X+X+15-X=100
=>105-100=X
=>X=5%

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