amanvermagmat wrote:
In a city, there are 400 people who are members of one or more of the three literary clubs: club L, club M and club P. 40 people are members of only club M, 80 people are members of only club L, and 90 people are members of only club P. How many of these 400 people are members of all three clubs?
(1) Out of those who are members of club M, ratio of those who are members of only this club to those who are members of exactly one more club along with M; is 1:2.
(2) People who are members of either club L or club P but not club M are 230 in number.
Let a = member of only club M = 40
b = member of only club L = 80
c = member of only club P = 90
d = member of club M & club L but not club P = not given
e = member of club L and club P but not M = not given
f = member of club P and club M but not club L = not given
g = member of all the three clubs
Next, a + b + c + d+ e + f+ g = 400
From first statement a/(d + e) = 1/2 and a = 40, therefore d + e = 80 but from this information we can't get the value of g as f is still unknown, hence A is out
From second statement a + f + c= 230, we know a and c so we can find f but d and e are still unknown so we can't find the value of g, hence B is out
next combining both
we have d + e = 80 and f = 60 and we know the value of a, b and c hence we can find out the value of g(Member of all the three clubs)
so the correct answer is C