amanvermagmat wrote:
A club has 80 members, each of which practice one or more of tennis, swimming and yoga. 41 practice tennis, 45 practice swimming while 49 practice yoga. How many practice all three activities?
(1) 35 practice exactly two activities out of the three.
(2) 35 practice exactly one activity out of the three.
Combined : Exactly one -35, exactly two-35, so exactly three would be 80-35-35=10.
two things-
1) What about the info -
41 practice tennis, 45 practice swimming while 49 practice yoga. . We have not used it at all.
2) Too easy a question for C, so could be a trap.
Advice : If short of time, and C is too obvious and each statement gives you a separate info, mark D.
let us draw Venn diagram ..
so \(a+b+c+d+e+f+g=80\).....(i)
from
41 practice tennis, 45 practice swimming while 49 practice yoga. , we get \((a+d+e+g)+(b+e+f+g)+(c+f+d+g)=41+45+49=135....... a+b+c+2(d+e+f)+3g=135....(ii)\)
we are looking for g.
(1) 35 practice exactly
two activities out of the three.
\(a+b+c+d+e+f+g=80\).....\(a+b+c+35+g=80\).....\(a+b+c+g=80-35=45\).....(i)(i)
\(a+b+c+2(d+e+f)+3g=135...........a+b+c+2(35)+3g=135..........a+b+c+3g=135-70=65....(ii)\)
subtract i from ii... 2g=20...g=10
sufficient
(2) 35 practice exactly
one activity out of the three.
\(a+b+c+d+e+f+g=80\).....\(35+d+e+f+g=80\).....\(d+e+f+g=80-35=45\).....(i)(i)
\(a+b+c+2(d+e+f)+3g=135...........35+2(d+e+f)+3g=135..........2(d+e+f)+3g=135-35=100....(ii)\)
multiply i with 2 and subtract from ii... g=100-2*45=10
sufficient
D
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