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?
DS - SETS
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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
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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total=5555 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.
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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- sivaelectric
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Insufficient hence E
If I am wrong correct me , If my post helped let me know by clicking the Thanks button .
Chitra Sivasankar Arunagiri
Chitra Sivasankar Arunagiri
- phanideepak
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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
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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You didn't consider p(none).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
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Cans, from where does p(none) fits into the equation above? pls explain..cans wrote:You didn't consider p(none).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
- phanideepak
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@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) ??
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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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.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?
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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Stuart Kovinsky wrote:Hello Stuart,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?
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?