DS - SETS

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DS - SETS

by MI3 » Mon May 16, 2011 12:04 pm
Q: 55 people live in an apartment complex with three fitness clubs (A, B, and C). Of the 55 residents, 40
residents are members of exactly one of the three fitness clubs in the complex. Are any of the 55 residents members of both fitness clubs A and C but not members of fitness club B?
(1) 2 of the 55 residents are members of all three of the fitness clubs in the apartment complex.
(2) 8 of the 55 residents are members of fitness club B and exactly one other fitness club in the
apartment complex.

Answer I chose: B, am I correct?

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by pankajks2010 » Mon May 16, 2011 6:47 pm
The question provides us the total number of people and the number of members of exactly one of the three fitness clubs.

Now, the equation can be framed as:

total number of people = members of individual clubs + members of two clubs - members of all the three clubs

To make it short, M=N+O-P
value for M&N is provided in the question. Statement 1 provides information on P alone and statement 2 provides partial information (as we still need to find out the common members from A&C) on O alone. Thus, both are individually insufficient. However, combining both, we can figure out the common members of A&C. Thus, Sufficient

Answer should be C. The common members of A&C would be 9

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by cans » Mon Jun 06, 2011 9:52 pm
55 people live in an apartment complex with three fitness clubs (A, B, and C). Of the 55 residents, 40
residents are members of exactly one of the three fitness clubs in the complex. Are any of the 55 residents members of both fitness clubs A and C but not members of fitness club B?
(1) 2 of the 55 residents are members of all three of the fitness clubs in the apartment complex.
(2) 8 of the 55 residents are members of fitness club B and exactly one other fitness club in the
apartment complex.
total=55
40-exactly one. it means 15 members either none or 2 or 3.
a)2 all 3. Thus 12 either none or 2 of A,B,C
As we don't know how main members belong to no club, insufficient
IMO E
insufficient.
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by sivaelectric » Mon Jun 06, 2011 10:43 pm
Insufficient hence E
If I am wrong correct me :), If my post helped let me know by clicking the Thanks button ;).

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by phanideepak » Tue Jun 07, 2011 3:11 am
IMO its C

total = p(only a) +p(only b) + p(only c) + p(only a and b) + p(only b and c) + p(only c and a) + p(only a,b and c)

p(only a) +p(only b) + p(only c) = 40
55 = 40 + p(only a and b) + p(only b and c) + p(only c and a) + p(only a,b and c)

we have been asked for p(only a and c)

a) p(only a,b and c) = 2
55 = 40 + p(only a and b) + p(only b and c) + p(only c and a) + 2 so insuff


b) p(only b and a) + p(only b and c) = 8
55 = 40 + 8 + p(only c and a) + p(only a,b and c) so insuff

combining a and b

55 = 40 + 8 + p(only c and a) + 2

p(only c and a) = 55 So answer is c

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by cans » Tue Jun 07, 2011 3:29 am
phanideepak wrote:IMO its C

total = p(only a) +p(only b) + p(only c) + p(only a and b) + p(only b and c) + p(only c and a) + p(only a,b and c)

p(only a) +p(only b) + p(only c) = 40
55 = 40 + p(only a and b) + p(only b and c) + p(only c and a) + p(only a,b and c)

we have been asked for p(only a and c)

a) p(only a,b and c) = 2
55 = 40 + p(only a and b) + p(only b and c) + p(only c and a) + 2 so insuff


b) p(only b and a) + p(only b and c) = 8
55 = 40 + 8 + p(only c and a) + p(only a,b and c) so insuff

combining a and b

55 = 40 + 8 + p(only c and a) + 2

p(only c and a) = 55 So answer is c
You didn't consider p(none).
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by krishnasty » Tue Jun 07, 2011 7:41 am
cans wrote:
phanideepak wrote:IMO its C

total = p(only a) +p(only b) + p(only c) + p(only a and b) + p(only b and c) + p(only c and a) + p(only a,b and c)

p(only a) +p(only b) + p(only c) = 40
55 = 40 + p(only a and b) + p(only b and c) + p(only c and a) + p(only a,b and c)

we have been asked for p(only a and c)

a) p(only a,b and c) = 2
55 = 40 + p(only a and b) + p(only b and c) + p(only c and a) + 2 so insuff


b) p(only b and a) + p(only b and c) = 8
55 = 40 + 8 + p(only c and a) + p(only a,b and c) so insuff

combining a and b

55 = 40 + 8 + p(only c and a) + 2

p(only c and a) = 55 So answer is c
You didn't consider p(none).
Cans, from where does p(none) fits into the equation above? pls explain..

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by phanideepak » Tue Jun 07, 2011 7:57 am
@Cans

It was not given that there are people who do not belong to any of the clubs so how did you consider p(none) ??

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by Stuart@KaplanGMAT » Tue Jun 07, 2011 10:49 am
MI3 wrote:Q: 55 people live in an apartment complex with three fitness clubs (A, B, and C). Of the 55 residents, 40
residents are members of exactly one of the three fitness clubs in the complex. Are any of the 55 residents members of both fitness clubs A and C but not members of fitness club B?
(1) 2 of the 55 residents are members of all three of the fitness clubs in the apartment complex.
(2) 8 of the 55 residents are members of fitness club B and exactly one other fitness club in the
apartment complex.

Answer I chose: B, am I correct?
Cans is dead on - nowhere does it say that every resident belongs to at least one fitness club, so we can't make that assumption.

It's actually very rare for 3-set questions on the GMAT to have a "none" component, which is why the formula doesn't usually worry about that possibility; the vast majority of such questions on the GMAT explicitly say that every item is a member of at least one of the 3 groups. However, as always, we can't make any assumptions in DS - since that information is not provided on this question, we can't assume that all residents must belong to a club.

So, as written, the answer is E - not enough info. What's the source of the question?
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by MI3 » Mon Jun 13, 2011 8:57 pm
Stuart Kovinsky wrote:
MI3 wrote:Q: 55 people live in an apartment complex with three fitness clubs (A, B, and C). Of the 55 residents, 40
residents are members of exactly one of the three fitness clubs in the complex. Are any of the 55 residents members of both fitness clubs A and C but not members of fitness club B?
(1) 2 of the 55 residents are members of all three of the fitness clubs in the apartment complex.
(2) 8 of the 55 residents are members of fitness club B and exactly one other fitness club in the
apartment complex.

Answer I chose: B, am I correct?
Hello Stuart,

Thank you for the explanation. The source of the problem is from one of the written content that I had found on the internet!

Cheers,
M


Cans is dead on - nowhere does it say that every resident belongs to at least one fitness club, so we can't make that assumption.

It's actually very rare for 3-set questions on the GMAT to have a "none" component, which is why the formula doesn't usually worry about that possibility; the vast majority of such questions on the GMAT explicitly say that every item is a member of at least one of the 3 groups. However, as always, we can't make any assumptions in DS - since that information is not provided on this question, we can't assume that all residents must belong to a club.

So, as written, the answer is E - not enough info. What's the source of the question?