jamifahad 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
We see that 144 - 89 = 55 residents could swim, 144 - 100 = 44 could dance and 144 - 91 = 53 could drive a car. We can use the formula:
Total = #(swim) + #(dance) + #(drive) - #(exactly two groups) - 2 * #(all three groups) + #(neither)
We need to find #(neither), so let’s denote it by n. We have the numbers for all the other components of the formula except for #(exactly two groups). That is because the number 37 represents #(at least two groups), in other words, 37 represents #(exactly two groups) + #(all three groups). So:
37 = #(exactly two groups) + 6
31 = #(exactly two groups)
Now, we can use the formula:
144 = 55 + 44 + 53 - 31 - 2*6 + n
144 = 109 + n
35 = n
Answer: D