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# Health Club has 250 members. 120 take part in swimming, 85

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Health Club has 250 members. 120 take part in swimming, 85 [#permalink]

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17 Dec 2003, 07:58
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Health Club has 250 members. 120 take part in swimming, 85 play tennis and 95 take part in aerobics. how many of the members participate in only two activities ?

A. 10 members play all three activities
B. 25 members participate in tennis and swimming, but not aerobics.

EDIT : I hope the numbers are fine now. thanks for your replies.
try solving the problem one statement at a time.

Last edited by Praetorian on 18 Dec 2003, 06:31, edited 5 times in total.
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17 Dec 2003, 08:18
E??
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17 Dec 2003, 08:34
Praetorian,

I think you need to restate your question

Health Club has 250 members. 110 take part in swimming, 75 of these play tennis and 95 of these take part in aerobics

I interpret "these" to mean: "the people who take part in swimming" and "that take part in tennis".

Two re-writes:
1) The Health Club has 250 members. 110 members take part in swimming. 75 members play tennis. 95 members take part in aerobics.

or,

2)Health Club has 250 members. 110 take part in swimming, 75 of the people who swim play tennis and 95 of the people who swim take part in aerobics.

Do you agree that your use of "these" is vague?
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17 Dec 2003, 09:48
Your question is impossible. To wit:

From the stem:

75 play tennis

From A and B:

A. 50 members plays all three activities
B. 45 members participate in tennis and swimming, but not aerobics.

This means at least 95 people play tennis. But the question says that only 75 play tennis!
CEO
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17 Dec 2003, 10:24
stoolfi wrote:
Your question is impossible. To wit:

From the stem:

75 play tennis

From A and B:

A. 50 members plays all three activities
B. 45 members participate in tennis and swimming, but not aerobics.

This means at least 95 people play tennis. But the question says that only 75 play tennis!

i am sorry, but i didnt understand too much of your observation

this is how i did it.

We know from the stem.

110 + 75 + 95 - ( ST + TA + SA ) + 2 * STA = 250

From 1

We know STA = 50
110 + 75 + 95 + 2*50 -250 = ST + TA + SA
130 = ST + TA + SA

So 1) is sufficient

From 2 alone ,

We know ST = 45 , which is clearly not sufficient.

my answer : A
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17 Dec 2003, 10:34
Quote:
i am sorry, but i didnt understand too much of your observation

How many people play tennis?

According to the question stem, there are only 75 people who play tennis.

But in part a you say that "50 members plays all three activities"
And in part b you say that "45 members participate in tennis and swimming, but not aerobics."

The number of people who play tennis equals
The number of people who play only tennis, plus
The number of people who do tennis and aerobics (but not swimming), plus
The number of people who do tennis and swimming (but not aerobics), plus
The number who do all three

But 75 only equals 50+45+TA+TS if TA and/or TS is negative.

And they can't be negative in a problem like this.
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17 Dec 2003, 11:22
praetorian123 wrote:
stoolfi wrote:
Your question is impossible. To wit:

From the stem:

75 play tennis

From A and B:

A. 50 members plays all three activities
B. 45 members participate in tennis and swimming, but not aerobics.

This means at least 95 people play tennis. But the question says that only 75 play tennis!

i am sorry, but i didnt understand too much of your observation

this is how i did it.

We know from the stem.

110 + 75 + 95 - ( ST + TA + SA ) + 2 * STA = 250

From 1

We know STA = 50
110 + 75 + 95 + 2*50 -250 = ST + TA + SA
130 = ST + TA + SA

So 1) is sufficient

From 2 alone ,

We know ST = 45 , which is clearly not sufficient.

my answer : A

How did you conclude (1) is sufficient. I got 130 for people those who don't play all the three together.
CEO
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17 Dec 2003, 12:22
stoolfi wrote:
Quote:
i am sorry, but i didnt understand too much of your observation

How many people play tennis?

According to the question stem, there are only 75 people who play tennis.
But in part a you say that "50 members plays all three activities"
And in part b you say that "45 members participate in tennis and swimming, but not aerobics."

The number of people who play tennis equals
The number of people who play only tennis, plus
The number of people who do tennis and aerobics (but not swimming), plus
The number of people who do tennis and swimming (but not aerobics), plus
The number who do all three

But 75 only equals 50+45+TA+TS if TA and/or TS is negative.

And they can't be negative in a problem like this.

Well, you assume that 45 and 50 are "Exclusive" , that is one's got nothing to do with the other. If you draw a venn diagram, you will see that some part of 45 members are a part of 50. But we dont know how many ,and as you very correctly pointed out, no negatives can exist.

Heres what i can say about composition of 75

75 = People playing ONLY tennis + People playing Tennis and Aerobics + People Playing Tennis and Swimming - People playing all three

(We double count the "all threes" , so we subtract the value once.)

Check this out using a venn diagram.
Please let me know if i am wrong.

Nice debate

Thanks so much
Praetorian
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17 Dec 2003, 12:25
Geethu wrote:
praetorian123 wrote:
stoolfi wrote:
Your question is impossible. To wit:

From the stem:

75 play tennis

From A and B:

A. 50 members plays all three activities
B. 45 members participate in tennis and swimming, but not aerobics.

This means at least 95 people play tennis. But the question says that only 75 play tennis!

i am sorry, but i didnt understand too much of your observation

this is how i did it.

We know from the stem.

110 + 75 + 95 - ( ST + TA + SA ) + 2 * STA = 250

From 1

We know STA = 50
110 + 75 + 95 + 2*50 -250 = ST + TA + SA
130 = ST + TA + SA

So 1) is sufficient

From 2 alone ,

We know ST = 45 , which is clearly not sufficient.

my answer : A

How did you conclude (1) is sufficient. I got 130 for people those who don't play all the three together.

130 for people who DONT play all the three together
can you show what you did.

Draw a venn diagram, it will be crystal clear.
just add the quantities and check if you counted something more than once..if you did subtract accordingly.
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17 Dec 2003, 14:47
I think the equestion needs to mention that there is nobody in the club who takes part in all three sports, so we can clearly understand the question and solve it.
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17 Dec 2003, 15:57
Preatorian,

I'm not trying to be a jerk here, but I really don't understand how

50 members plays all three activities
45 members participate in tennis and swimming, but not aerobics.

Are not exclusive of one another.

What would someone have to do to be a member of both groups?
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17 Dec 2003, 18:35
stoolfi wrote:
Preatorian,

I'm not trying to be a jerk here, but I really don't understand how

50 members plays all three activities
45 members participate in tennis and swimming, but not aerobics.

Are not exclusive of one another.

What would someone have to do to be a member of both groups?

Yes, Question steam has logical issue. The numbers won't add up.
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18 Dec 2003, 02:54
It seems to me that numbers are a bit wrong:

110+95+75=280 but if we subtract from it the number of club members, which is 250 it gives us 280-250= 30 And it's already less than 50 (members who does all of three activities). However, 30 must include not only those who do all three but also those with two activities

Please, correct me if I am wrong
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me

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18 Dec 2003, 04:27
stoolfi wrote:
Preatorian,

I'm not trying to be a jerk here, but I really don't understand how

50 members plays all three activities
45 members participate in tennis and swimming, but not aerobics.

Are not exclusive of one another.

What would someone have to do to be a member of both groups?

i guess a famous test prep company screwed up quite a bit here.
you are right, i am sorry about that.
45 and 50 are indeed exclusive.
i got mixed up with the {but not aerobics thing}
i will try to change the problem.

But then i could solve the problem with just statement 1 taken alone.
and when i considered statement 2 seperately , it didnt matter.

So i never had to consider both statements together. see what i am saying

but yes, if you do take both the statements together, the problem does not have a logical solution.

i hate this test prep company now.

sorry guys
praetorian
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Re: DS : Health Club [#permalink]

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19 Dec 2003, 02:44
praetorian123 wrote:
Health Club has 250 members. 120 take part in swimming, 85 play tennis and 95 take part in aerobics. how many of the members participate in only two activities ?

A. 10 members play all three activities
B. 25 members participate in tennis and swimming, but not aerobics.

EDIT : I hope the numbers are fine now. thanks for your replies.
try solving the problem one statement at a time.

It could have been A but for a fact that some members may in fact participate in none of the activities. So, I opt for E.
Re: DS : Health Club   [#permalink] 19 Dec 2003, 02:44
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# Health Club has 250 members. 120 take part in swimming, 85

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