swerve wrote:A survey was conducted to find out how many people in a housing colony of 144 residents could swim, dance a 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
The OA is D.
Please, can any expert explain this PS question for me? I have many difficulties to understand why that is the correct answer. Thanks.
let us take number of people who could only swim = a
...........................................................................................drive = b
...........................................................................................dance = c
...........................................................................................swim and drive = d
............................................................................................drive and dance= e
...........................................................................................dance and swim = f
..................................................................................not do any of the items= Z
number of people who know swiming+driving+dancing = 6
......................................................... at least two items = 37
therefore a+b+c+d+e+f+Z+6= 144
and d+e+f = 37 - 6 = 31
therefore a+b+c+ 31 +Z+6= 144
or a+b+c = 107- Z
those who could not swim = 89
therefore b+c+e+ Z = 89
Similaly a+c+f+ Z = 91
and a+b+d+ Z = 100
Adding we get 2(a+b+c) + (d+e+f) + 3Z =280
or 2(107-Z) + 31 + 3Z = 280
This gives Z = 280 - 214-31 = 35
Hence D is the correct answer
