Problem Solving

LalaB wrote: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 is D

Given:
# of swimmers = 144 - 89 = 55
# of dancers = 144 - 100 = 44
# of drivers = 144 - 91 = 53

Let's sketch the overlapping sets and use whatever numbers satisfy the given information. To do this, I start at the very middle (person does all 3) and place a 6.


From here, we know that the areas where there are exactly two overlaps must add to 31 since there are 37 people who do 2 or more activities. So, I used the values 20, 10 and 1 to satisfy that given condition. Note: I could have used any 3 numbers that add to 31; the result will still be the same - try it.


At that point, we need to fill in the remaining parts of the circles based on the number of people who do each activity. When we do so, we get this.


When we add up the different sections, we get:
17+10+6+20+17+1+38 = 109

So, we've now accounted for 109 people out of 144 people.
So, the remaining 35 people must not do any of these activities.

Answer = D

Cheers,
Brent