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03 Jul 2025, 02:46
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Option C is the correct answer.
First of all lets understand the question and what we need to find in order to answer it. So lets use Venn Diagram for better understanding
So as we can see in this Venn diagram that the total number of people who have enrolled in Archery are (A+x+y+w), Swimming (S+z+w+y) and Hiking (H+x+z+w).
Now lets check what the question is asking from us. So the question is basically asking us "Among those enrolled in Archery, what fraction are also enrolled in Swimming". Which means what is the value of y/(A+x+y+w) and from the question we know that the ratio of Hiking:Swiming:Archery is 5:6:11. Or we can write it as H = 5g, S = 6g, A = 11g
At first look it seems pretty easy right, like the answer to the question is a simple 6:11 but this is exactly what makes it most incorrect assumption because as we can see in the Veen Diagram that there are overlaps in the set. Might be some students have enrolled in all 3 activities and as per the question those cases can not be considered while answering the question because the question asks us about the overlap of only Archery and Swimming.
So now lets check the given statements and try to find the whether we can get unique value to answer the question or not.
Statement 1: "All students enrolled in Hiking are also enrolled in Archery".
This statement tells us that all the students who have enrolled in Hiking have also enrolled in Archery as well but does not tell us anything about the overlap between Swimming and Archery. So this is Not Sufficient.
Statement 2: "Every student enrolled in Archery is also enrolled in at least one other group".
This statement tells us that all the students who have enrolled in Archery have also enrolled in atlest one other activity which means either the students have enrolled and Archery & Swimming, Archery & Hiking or in all 3 of them. Which also does not gives us any unique value to rely on.
If you are still confused with this statement then lets understand it with the help of some examples.
Total Student = Archery + Swimming + Hiking - (All students enrolled in any 2 activities) + (Students enrolled in all 3 activities) + Neither (Which is 0)
As from statement 2 we know each Archery student enrolled in atlest 1 other activity so the total of 'All students enrolled in any 2 activities' & 'Students enrolled in all 3 activities' will be 11 which can create multiple cases like (1,10), (2,9), (3,8) and so on. And from here also if we can have value of multiple 'All students enrolled in any 2 activities' for which x, y, z will also multiple case values.
So this statement also does not give us any unique value. So this is Not Sufficient.
Now as we know that both the statements on their own is not sufficient to answer the question then Lets check if the Combination will give us any unique value or not.
So as from both the statements we know that all the students enrolled in Archery also take classes from atlest 1 other activity and all the students in Hiking activity takes classes of Archery. Then from here we can calculate the unique number of students who take classes from only Archery and Swimming activity. Which will be 11g - 5g = 6g (Number of students attending only Archery and Swimming classes).
So the fraction of Archery student who also enrolled in Swimming will be: 6g/11g.
Since we know that the number of students is not '0' so we can cancel out 'g' and get 6/11 as our answer. Which means both statement alone are insufficient but the Combination of both is sufficient to answer the question (Option C).
GMAT-Club-Forum-5kifyhlj.png [ 12.31 KiB | Viewed 191 times ]
First of all lets understand the question and what we need to find in order to answer it. So lets use Venn Diagram for better understanding
So as we can see in this Venn diagram that the total number of people who have enrolled in Archery are (A+x+y+w), Swimming (S+z+w+y) and Hiking (H+x+z+w).
Now lets check what the question is asking from us. So the question is basically asking us "Among those enrolled in Archery, what fraction are also enrolled in Swimming". Which means what is the value of y/(A+x+y+w) and from the question we know that the ratio of Hiking:Swiming:Archery is 5:6:11. Or we can write it as H = 5g, S = 6g, A = 11g
At first look it seems pretty easy right, like the answer to the question is a simple 6:11 but this is exactly what makes it most incorrect assumption because as we can see in the Veen Diagram that there are overlaps in the set. Might be some students have enrolled in all 3 activities and as per the question those cases can not be considered while answering the question because the question asks us about the overlap of only Archery and Swimming.
So now lets check the given statements and try to find the whether we can get unique value to answer the question or not.
Statement 1: "All students enrolled in Hiking are also enrolled in Archery".
This statement tells us that all the students who have enrolled in Hiking have also enrolled in Archery as well but does not tell us anything about the overlap between Swimming and Archery. So this is Not Sufficient.
Statement 2: "Every student enrolled in Archery is also enrolled in at least one other group".
This statement tells us that all the students who have enrolled in Archery have also enrolled in atlest one other activity which means either the students have enrolled and Archery & Swimming, Archery & Hiking or in all 3 of them. Which also does not gives us any unique value to rely on.
If you are still confused with this statement then lets understand it with the help of some examples.
Total Student = Archery + Swimming + Hiking - (All students enrolled in any 2 activities) + (Students enrolled in all 3 activities) + Neither (Which is 0)
As from statement 2 we know each Archery student enrolled in atlest 1 other activity so the total of 'All students enrolled in any 2 activities' & 'Students enrolled in all 3 activities' will be 11 which can create multiple cases like (1,10), (2,9), (3,8) and so on. And from here also if we can have value of multiple 'All students enrolled in any 2 activities' for which x, y, z will also multiple case values.
So this statement also does not give us any unique value. So this is Not Sufficient.
Now as we know that both the statements on their own is not sufficient to answer the question then Lets check if the Combination will give us any unique value or not.
So as from both the statements we know that all the students enrolled in Archery also take classes from atlest 1 other activity and all the students in Hiking activity takes classes of Archery. Then from here we can calculate the unique number of students who take classes from only Archery and Swimming activity. Which will be 11g - 5g = 6g (Number of students attending only Archery and Swimming classes).
So the fraction of Archery student who also enrolled in Swimming will be: 6g/11g.
Since we know that the number of students is not '0' so we can cancel out 'g' and get 6/11 as our answer. Which means both statement alone are insufficient but the Combination of both is sufficient to answer the question (Option C).
Bunuel
Attachment:
GMAT-Club-Forum-5kifyhlj.png [ 12.31 KiB | Viewed 191 times ]
03 Jul 2025, 02:58
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Let the number of students in Hiking = 5x, Swimming = 6x, Archery = 11x.
Let N be the total number of students.
Statement (1) Alone:
All hikers are archers: H⊆A so all 5x hikers are among the 11xarchers.
But we don't know how many archers are also swimmers, or how many are in all three groups.
Not sufficient.
Statement (2) Alone:
Every archer is in at least one other group (Hiking or Swimming or both).
So, number of students in only Archery = 0.
But we still don't know the overlap between Archery and Swimming.
Not sufficient.
So we can eliminate option (A),(B) & (D)
If we combine both statements,
Then we have 5x archers who are also part of hiking as per statement 1. But we are also given that every Archer is part of at least one other group & there are only 2 other groups other than Archery. This means that out of 11x Archers, 11x-5x = 6x archers are also swimmers. Hence the fraction of archers who are swimmers is 6x/11x = 6/11
Hence option (C) is sufficient & is the correct answer
Let N be the total number of students.
Statement (1) Alone:
All hikers are archers: H⊆A so all 5x hikers are among the 11xarchers.
But we don't know how many archers are also swimmers, or how many are in all three groups.
Not sufficient.
Statement (2) Alone:
Every archer is in at least one other group (Hiking or Swimming or both).
So, number of students in only Archery = 0.
But we still don't know the overlap between Archery and Swimming.
Not sufficient.
So we can eliminate option (A),(B) & (D)
If we combine both statements,
Then we have 5x archers who are also part of hiking as per statement 1. But we are also given that every Archer is part of at least one other group & there are only 2 other groups other than Archery. This means that out of 11x Archers, 11x-5x = 6x archers are also swimmers. Hence the fraction of archers who are swimmers is 6x/11x = 6/11
Hence option (C) is sufficient & is the correct answer
SSWTtoKellogg
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Schools: Kellogg INSEAD Jan '26 Ross '26 Duke '26 Darden '26 Anderson '26 Tepper '26 Johnson '26 Kelley '26
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03 Jul 2025, 03:13
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We need S & A /11n.
S1 : It might be tempting that 6n of Swimming would also come under 11n of A. But we don't know what whether all swimming of 6n inside 11n or not. (NS)
S2 : If A (11n) are has to be one of the other, then all swimming 6n has to be within 11n. (S)
B
S1 : It might be tempting that 6n of Swimming would also come under 11n of A. But we don't know what whether all swimming of 6n inside 11n or not. (NS)
S2 : If A (11n) are has to be one of the other, then all swimming 6n has to be within 11n. (S)
B
