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# A club has 80 members, each of which practice one or more of tennis,

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Retired Moderator
Joined: 22 Aug 2013
Posts: 1434
Location: India
A club has 80 members, each of which practice one or more of tennis,  [#permalink]

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08 Dec 2018, 22:58
1
5
00:00

Difficulty:

95% (hard)

Question Stats:

26% (02:14) correct 74% (02:04) wrong based on 58 sessions

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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.
Math Expert
Joined: 02 Aug 2009
Posts: 7756
Re: A club has 80 members, each of which practice one or more of tennis,  [#permalink]

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08 Dec 2018, 23:54
1
1
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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Joined: 23 Apr 2019
Posts: 22
Re: A club has 80 members, each of which practice one or more of tennis,  [#permalink]

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23 Jul 2019, 06:14
1
1
Hi,

When a Venn Diagram question asks us to find the overall intersection, the best way to solve the question is to visualize the regions of the Venn diagram rather than use variables to solve.

Let us break down the question here:

Attachment:

Capture 1.PNG [ 34.95 KiB | Viewed 249 times ]

We have a + b + c + 2x = 55 and the question here asks us to find the value of x.

Statement 1: 35 practice exactly two activities out of the three.

Given a + b + c = 35

This clearly is sufficient to solve for x.

Statement 2: 35 practice exactly one activity out of the three.

Attachment:

Capture 2.PNG [ 31.96 KiB | Viewed 248 times ]

We have a + b + c + x = 45 and from the question stem we have a + b + c + 2x = 55 ----> a + b + c + x + x = 55 ----> 45 + x = 55 ----> x = 10.

Sufficient.

Re: A club has 80 members, each of which practice one or more of tennis,   [#permalink] 23 Jul 2019, 06:14
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