In a city, there are 400 people who are member of one or more of three

Question

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.

u1983 · Answer

According to question :
x=80 , y=40 , z=90
According to the picture above : x+y+z+a+b+c+m=400
Thus , a+b+c+m=400-(x+y+z)=400-210=190
 According to the Q-stem m = ?

1) y:(b+c)=1:2
 y=40
hence, (b+c)=80
still no information about a or m......... .......(NS)

2) x+y+a=230
 x+y=120
hence, a=110
still no information about (b+c) or m............ ....(NS)

1+2) we have a,(b+c) we can find m ............. Thus Sufficient

Hence I would go for answer C.

zishu912 · Answer

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

AkshdeepS · Answer

Why did you choose d+e for statement and not e+f or d+f? I am a little bit confused in statement 1.

QZ

zishu912 · Answer

IMG_20180527_023715.jpg Since the statement says the ratio of m only to members along with of m (out of people who are members of the club m)

gvij2017 · Answer

I have a little doubt here...

1st ...question said either L or P but not M.....means 80 + 90= 230.....that is wrong here. It must be Members of L and P but not M
2nd you did 80 +40+a= 230....but it should be 80+90+a= 230

Please clear my doubts.

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In a city, there are 400 people who are member of one or more of three

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