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A survey

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A survey

by gmatblood » Sat Oct 29, 2011 11:51 am
A survey was conducted to find out how many people in a housing colony of 144 residents could swim, dance and drive a car. It was found that the number of people who could not swim was 89, the number of people who could not dance was 100 and that the number of people who could not drive a car was 91. If the number of people who could do at least two of these things, was found to be 37 and the number of people who could do all these things was found to be 6, how many people could not do any of these things?

A) 17

B) 23

C) 29

D) 35

E) 50

OA: D
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by rijul007 » Sat Oct 29, 2011 12:31 pm
According to the venn diagram
Image


a+b+c+d+e+f+g+x = 144-----[1]

Non swimming:
b+f+c+x = 89

Non dancing:
a+c+e+x = 100

Non driving:
a+d+b+x = 91

adding all the three equations=>
2(a+b+c)+d+e+f+3x = 280 --------[2]


people who do atleast 2 things =>
d+e+f+g = 37
g = 6

d+e+f = 31 ------[3]

substituting this in eq 1
a+b+c+x = 144-37 = 107 ------[4]

substuting [3] in [2]
2(a+b+c)+31+3x=280
2(a+b+c)+3x = 280-31 = 249----[5]

3*[4] - [5]
3(a+b+c)+3x -[2(a+b+c) + 3x] = 321-249
a+b+c = 72
x=35

Option D
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