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Within a class, 50 percent of students are members of Club #30 and 60 29 Aug 2019, 07:03
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95% (hard)

Question Stats:

47% (02:36) correct 53% (02:33) wrong based on 87 sessions

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Within a class, 50 percent of students are members of Club #30 and 60 percent are members of Club #50. If 30 percent of the members of Club #50 are members of Club #60, how many of the members of Club #60 are members of Club #50?

(1) One hundred of the students are members of Club #30.

(2) Twenty-five percent of the non-members of Club #50 are members of Club #60.
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A
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Within a class, 50 percent of students are members of Club #30 and 60 Updated on: 14 Sep 2019, 02:09
Originally posted by Kinshook on 29 Aug 2019, 09:57.
Last edited by Kinshook on 14 Sep 2019, 02:09, edited 1 time in total.
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Bunuel
Within a class, 50 percent of students are members of Club #30 and 60 percent are members of Club #50. If 30 percent of the members of Club #50 are members of Club #60, how many of the members of Club #60 are members of Club #50?

(1) One hundred of the students are members of Club #30.

(2) Twenty-five percent of the non-members of Club #50 are members of Club #60.
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Given:
1. Within a class, 50 percent of students are members of Club #30
2. 60 percent are members of Club #50.
3. 30 percent of the members of Club #50 are members of Club #60.

Asked: How many of the members of Club #60 are members of Club #50?

Let the total members be T.

Members of club#30 = .5T
Members of club#50 = .6T
Members of club#50 & club#60 = .3(.6T) = .18T

(1) One hundred of the students are members of Club #30.
0.5T = 100
T = 200
0.18T = 36
SUFFICIENT


(2) Twenty-five percent of the non-members of Club #50 are members of Club #60.
.25(.4T) = .1T
Total members of club#60 = .1T + .18T = .28T
Number of the members of Club #60 are members of Club #50 = .18T
Since T is unknown.
NOT SUFFICIENT

IMO A

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Within a class, 50 percent of students are members of Club #30 and 60 31 Aug 2019, 07:45
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Hello Bunuel can you give a detailed explanation for this one please ?
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Within a class, 50 percent of students are members of Club #30 and 60 Updated on: 14 Sep 2019, 02:02
Originally posted by Kinshook on 08 Sep 2019, 05:43.
Last edited by Kinshook on 14 Sep 2019, 02:02, edited 1 time in total.
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Bunuel
Within a class, 50 percent of students are members of Club #30 and 60 percent are members of Club #50. If 30 percent of the members of Club #50 are members of Club #60, how many of the members of Club #60 are members of Club #50?

(1) One hundred of the students are members of Club #30.

(2) Twenty-five percent of the non-members of Club #50 are members of Club #60.
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Bunuel OA needs to be corrected to B

Given:
1. Within a class, 50 percent of students are members of Club #30
2 60 percent are members of Club #50.
3. 30 percent of the members of Club #50 are members of Club #60

Asked: How many of the members of Club #60 are members of Club #50?

Let the total members be T
Members of club#30 = .5T
Members of club#50 = .6T
Members of club#50 and club#60 = .3(.6T) = .18T


(1) One hundred of the students are members of Club #30.
.5T = 100
T = 200
.18T = 36
SUFFICIENT

(2) Twenty-five percent of the non-members of Club #50 are members of Club #60.
.25(.4T) = .1T
Total members of club#60 = .1T + .18T = .28T
Number of the members of Club #60 are members of Club #50 = .18T
Since T is unknown.
NOT SUFFICIENT

IMO A
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Within a class, 50 percent of students are members of Club #30 and 60 08 Sep 2019, 09:15
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Hello Bunuel,

I am not able to understand the solution provided. Please help .
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Within a class, 50 percent of students are members of Club #30 and 60 09 Sep 2019, 01:54
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Kinshook
Bunuel
Within a class, 50 percent of students are members of Club #30 and 60 percent are members of Club #50. If 30 percent of the members of Club #50 are members of Club #60, how many of the members of Club #60 are members of Club #50?

(1) One hundred of the students are members of Club #30.

(2) Twenty-five percent of the non-members of Club #50 are members of Club #60.


Bunuel OA needs to be corrected to B
Please refer my solution above and in the image.
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The second statement cannot be sufficient because of a simple reason. We are asked to find the NUMBER of the members of Club #60 who are members of Club #50. From (2) we only know percentages, not a single numerical value of any group is given.
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Within a class, 50 percent of students are members of Club #30 and 60 09 Sep 2019, 01:56
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Kinshook
Bunuel
Within a class, 50 percent of students are members of Club #30 and 60 percent are members of Club #50. If 30 percent of the members of Club #50 are members of Club #60, how many of the members of Club #60 are members of Club #50?

(1) One hundred of the students are members of Club #30.

(2) Twenty-five percent of the non-members of Club #50 are members of Club #60.

Given:
1. Within a class, 50 percent of students are members of Club #30
2. 60 percent are members of Club #50.
3. 30 percent of the members of Club #50 are members of Club #60.

Asked: How many of the members of Club #60 are members of Club #50?

----------------------Club 50 -------------Club 50 X---------------Total
Club 30 ------------- \ ------------- \ ---------------50%
Club 30 X----------- \ ------------- \ ---------------50%
Total ---------------- 60% ------------- 40% ---------------100%

----------------------Club 50 -------------Club 50 X------------------Total
Club 60 ------------- 18% ------------- x%-18% --------------- x%
Club 60 X----------- 42% ------------- 58% - x% ---------------100% - x%
Total ---------------- 60% ------------- 40% --------------------100%

(1) One hundred of the students are members of Club #30.

Total students = 100 /50% = 200 students

----------------------Club 50 -------------Club 50 X---------------Total
Club 30 ------------- \ ------------- \ ---------------50%
Club 30 X----------- \ ------------- \ ---------------50%
Total ---------------- 60% ------------- 40% ---------------100% = 200

----------------------Club 50 --------------------Club 50 X-----------------------Total
Club 60 ------------- 18% =36 ------------- x% -18% =2x -36 --------------- x% =2x
Club 60 X----------- 42% =84 ------------- 58% -x% =116 -2x---------------100% - x% = 200 -2x
Total ---------------- 60% =120 ------------- 40% =80 ---------------------100% =200

Since x is unknown
NOT SUFFICIENT


(2) Twenty-five percent of the non-members of Club #50 are members of Club #60.

----------------------Club 50 -------------Club 50 X------------------Total
Club 60 ------------- 18% ------------- x%-18% --------------- x%
Club 60 X----------- 42% ------------- 58% - x% ---------------100% - x%
Total ---------------- 60% ------------- 40% --------------------100%

25% * 40% = 10% = x% - 18% ; x% = 28%

Number of the members of Club #60 are members of Club #50 = 18%/28% = 9/14
SUFFICIENT

IMO B

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Official Explanation



This question is made confusing by the fact that the clubs are numbered, creating a profusion of irrelevant digits in the question. Let's call the clubs Th, F, and S, for the first letters of thirty, fifty, and sixty. Also, since we are talking about the overlap of group memberships, we are in Venn diagram territory. Let's sketch it out and fill in what we can:



We could find FS, as we are being asked, by getting T. And there might be another way to find it, as well, though we are missing a lot of information. Let's look at the data statements, starting separately.

Statement (1) tells us the number of members in the first club. In other words, . That allows us to calculate T, from which we can calculate FS. So Statement (1) is sufficient.

Statement (2), in terms of the diagram, tells us the number of members of the bottom circle, S, outside of the portion we are looking for. The members of F are 60% of the total, so the non-members of F are 40% of the total, or 0.4T, and 25% of that amount is 0.1T. The problem is that this statement doesn't help us know T. It gets us closer to the total membership of S, but we're not even looking for that. We can see in analysis by cases: we can imagine that T is small or very large. Both are permitted by the data and lead to different answers for the overlap of F and S. Therefore, Statement (2) is insufficient.

The correct answer is (A).

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Within a class, 50 percent of students are members of Club #30 and 60 09 Sep 2019, 01:57
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Coggi
Hello Bunuel can you give a detailed explanation for this one please ?
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Within a class, 50 percent of students are members of Club #30 and 60 26 May 2024, 12:36
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