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At a certain health club, 30% of the members use both pool a

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At a certain health club, 30% of the members use both pool a  [#permalink]

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New post Updated on: 21 May 2017, 14:08
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At a certain health club, 30 percent of the members use both the pool and sauna, but 40 percent of the members who use the pool do not use the sauna. What percent of the members of the health club use the pool?

A. 33 1/3%
B. 40%
C. 50%
D. 62 1/2%
E. 75%


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Originally posted by raghavs on 07 Mar 2010, 10:25.
Last edited by Bunuel on 21 May 2017, 14:08, edited 2 times in total.
Renamed the topic, edited the question and added the OA.
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Re: At a certain health club, 30% of the members use both pool a  [#permalink]

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New post 07 Mar 2010, 11:21
raghavs wrote:
help me to get this.


well the wording is confusing (atleast to me :| )

giving it a try

P = pool S = sauna
given P+S = 30 then let only S be x and only P will be 100 - (30+x) = 70 -x
40% of (70-x) = x => 28 - 0.4x = x => x = 20% so only P = 70 -x = 50%
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Re: At a certain health club, 30% of the members use both pool a  [#permalink]

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New post 08 Mar 2010, 14:16
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raghavs wrote:
help me to get this.


Its given 30% use both pool and suana.

Also it is given 40% of the pool do not use sauna. Therefore 60% of the people who use pool also use sauna.

Let total no of members be 100
members using both pool & sauna = 30

Let no of members using Pool be p

60% of p = 30
p = 50
Therefore.. members using only Sauna = 100 -50 = 50
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Re: At a certain health club, 30% of the members use both pool a  [#permalink]

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New post 15 Apr 2014, 03:39
This problem belongs to overlapping sets not to percentage and interest.
by using tabular method with row : pool -- nopool and column: sauna | nosauna and by assuming total of members=100, one can easily solve this problem.
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Re: At a certain health club, 30% of the members use both pool a  [#permalink]

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New post 27 Apr 2014, 13:05
1
This question got me - I misunderstood the fact that 40% represents all people using the pool and the 30% represent the entire club members.

I'm trying to figure it out in another way to help me understand (although the overlapping sets method with the tables is probably the best)...

1. Let's assume that a total of 100 people use the pool.
2. From the question, 40% of them use the pool ONLY meaning 0.4 x 100 = 40 people. This means that 100-40=60 people uses the pool and sauna.
3. Also from the question, 30% of the ENTIRE CLUB uses the pool and sauna. If the 60 people from step 2 above uses the pool and sauna represents 30% of the entire club, that means there are 200 people in the club.
4. To find percentage of ALL people using the pool - 100/200 = 50%
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Re: At a certain health club, 30% of the members use both pool a  [#permalink]

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New post 28 Apr 2014, 06:42
raghavs wrote:
At a certain health club, 30 percent of the members use both the pool and sauna, but 40 percent of the members who use the pool do not use the sauna. What percent of the members of the health club use the pool?

A. 33 1/3%
B. 40%
C. 50%
D. 62 1/2%
E. 75%


Bunuel could you please help
i still find the question unclear
thank you
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Re: At a certain health club, 30% of the members use both pool a  [#permalink]

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New post 28 Apr 2014, 10:43
adymehta29 wrote:
raghavs wrote:
At a certain health club, 30 percent of the members use both the pool and sauna, but 40 percent of the members who use the pool do not use the sauna. What percent of the members of the health club use the pool?

A. 33 1/3%
B. 40%
C. 50%
D. 62 1/2%
E. 75%


Bunuel could you please help
i still find the question unclear
thank you


40 percent of the members who use the pool do not use the sauna, hence the remaining 60 percent of the members who use the pool use the sauna. So, 60 percent of the members who use the pool use both pool and sauna. So, 0.6*{pool} = {both}.

We also know that 30 percent of the members use both the pool and sauna: 0.3*{total} = {both}.

Equate: 0.6*{pool} = 0.3*{total} --> {pool}/{total} = 0.5.

Answer: C.

Hope it's clear.
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Re: At a certain health club, 30% of the members use both pool a  [#permalink]

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New post 12 Jul 2017, 09:02
Bunuel wrote:
adymehta29 wrote:
raghavs wrote:
At a certain health club, 30 percent of the members use both the pool and sauna, but 40 percent of the members who use the pool do not use the sauna. What percent of the members of the health club use the pool?

A. 33 1/3%
B. 40%
C. 50%
D. 62 1/2%
E. 75%


Bunuel could you please help
i still find the question unclear
thank you



40 percent of the members who use the pool do not use the sauna, hence the remaining 60 percent of the members who use the pool use the sauna


BUT THOSE 60% must contain people who do not use the pool and only use sauna?
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Re: At a certain health club, 30% of the members use both pool a  [#permalink]

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New post 16 Jul 2017, 17:25
raghavs wrote:
At a certain health club, 30 percent of the members use both the pool and sauna, but 40 percent of the members who use the pool do not use the sauna. What percent of the members of the health club use the pool?

A. 33 1/3%
B. 40%
C. 50%
D. 62 1/2%
E. 75%


We can let the total number of members = 100 and x = the number of members who use the pool.

Thus, we have 30 members who use both the pool and sauna. Since 40 percent of the members who use the pool do not use the sauna, we know that 60 percent of the members who use the pool also use the sauna, and we already know that this number is 30. Thus, we can create the following equation:

0.6x = 30

x = 30/0.6 = 300/6 = 50

Thus, 50/100 = 50% of the members use the pool.

Answer: C
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Re: At a certain health club, 30% of the members use both pool a  [#permalink]

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New post 24 Jul 2017, 09:13
One way to look at this:
- 40 = pool
- 30 = pool + sauna
- 60 = sauna (100 minus 40)

so how many pool? Pool users total = pool + pool - (pool+sauna overlap) => 40 + (40 - 30) = 50%
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Re: At a certain health club, 30% of the members use both pool a   [#permalink] 24 Jul 2017, 09:13
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