cleetus wrote:
This is a simple question to answer. Just thought of posting it with solution.
In a survey of political preferences, 78% of those asked were in favour of at least one of the proposals:
I, II and III. 50% of those asked favoured proposal I, 30% favoured proposal II, and 20% favoured proposal III. If 5% of those asked favoured all three of the proposals, what percentage of those asked favoured more than one of the 3 proposals.
(A) 10 (B) 12 (C) 17 (D) 22 (E) 30
My solution -
5% of those asked favoured all three of the proposals. The statement does not say that the exactly 5% of the people favoured all three of the proposals. Hence we can apply following formula.
x = I n II + II n III + I n III
5 is I n II n III
78 = 50 + 30 + 20 - x + 5
x = 27. In this value of 27 the intersection between all three sets is counted 3 times so substract it two times i.e., substract 2 *5 = 10
Total folks in favour of two or more proposals = 27 - 10 = 17