Bunuel wrote:
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
Posted from my mobile deviceThis 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.
close
29 Aug 2019, 07:03
58%
(02:26)
wrong 
