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28 Apr 2024, 22:38
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
46% (03:00) correct
54%
(03:03)
wrong
based on 121
sessions
History
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Time
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Not Attempted Yet
In a certain sports club, at least 50 members play cricket, and 70 members play football. 20 percent of the members who play both cricket and football also play volleyball. Do more members at the club play football than cricket if 20 members play both cricket and football?
(1) 40 percent of the members who play cricket and volleyball also play football.
(2) Number of members who play only cricket is less than half the number of members who play football. its a gmat data sufficiency question
(1) 40 percent of the members who play cricket and volleyball also play football.
(2) Number of members who play only cricket is less than half the number of members who play football. its a gmat data sufficiency question
29 Apr 2024, 01:15
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asdasdsf
Given: In a certain sports club, at least 50 members play cricket, and 70 members play football. 20 percent of the members who play both cricket and football also play volleyball.
Asked: Do more members at the club play football than cricket if 20 members play both cricket and football?
Screenshot 2024-04-29 at 1.34.38 PM.png [ 45.74 KiB | Viewed 4367 times ]
(1) 40 percent of the members who play cricket and volleyball also play football.
Screenshot 2024-04-29 at 1.36.52 PM.png [ 47.03 KiB | Viewed 4355 times ]
x + 26 >=50
But it can not be ascertained whether 70>x+26 or not
It can not be concluded whether more members at the club play football than cricket.
NOT SUFFICIENT
(2) Number of members who play only cricket is less than half the number of members who play football.
Screenshot 2024-04-29 at 1.41.47 PM.png [ 46.75 KiB | Viewed 4291 times ]
It can not be ascertained whether 70 > x+z+20 or not
NOT SUFFICIENT
(1) + (2)
(1) 40 percent of the members who play cricket and volleyball also play football.
(2) Number of members who play only cricket is less than half the number of members who play football.
Screenshot 2024-04-29 at 1.43.48 PM.png [ 47.65 KiB | Viewed 4220 times ]
x < 35
x + 26 < 35 + 26 = 61 < 70
More members at the club play football than cricket.
SUFFICIENT
IMO C
Given: In a certain sports club, at least 50 members play cricket, and 70 members play football. 20 percent of the members who play both cricket and football also play volleyball.
Asked: Do more members at the club play football than cricket if 20 members play both cricket and football?
Attachment:
Screenshot 2024-04-29 at 1.34.38 PM.png [ 45.74 KiB | Viewed 4367 times ]
(1) 40 percent of the members who play cricket and volleyball also play football.
Attachment:
Screenshot 2024-04-29 at 1.36.52 PM.png [ 47.03 KiB | Viewed 4355 times ]
But it can not be ascertained whether 70>x+26 or not
It can not be concluded whether more members at the club play football than cricket.
NOT SUFFICIENT
(2) Number of members who play only cricket is less than half the number of members who play football.
Attachment:
Screenshot 2024-04-29 at 1.41.47 PM.png [ 46.75 KiB | Viewed 4291 times ]
It can not be ascertained whether 70 > x+z+20 or not
NOT SUFFICIENT
(1) + (2)
(1) 40 percent of the members who play cricket and volleyball also play football.
(2) Number of members who play only cricket is less than half the number of members who play football.
Attachment:
Screenshot 2024-04-29 at 1.43.48 PM.png [ 47.65 KiB | Viewed 4220 times ]
x < 35
x + 26 < 35 + 26 = 61 < 70
More members at the club play football than cricket.
SUFFICIENT
IMO C
29 Apr 2024, 01:19
Kudos
Bookmarks
asdasdsf
Refer to the Venn diagram given below
Attachment:
Screenshot 2024-04-29 132804.png [ 31.45 KiB | Viewed 4135 times ]
- F → Only Football
- C → Only Cricket
- V → Only Volleyball
- FC → Football + Cricket
- FV → Football + Volleyball
- CV → Cricket + Volleyball
- FVC → Football + Cricket + Volleyball
C + CV + FCV \(\geq 50\)
70 members play football
F + FC + FV + FCV = 70
20 percent of the members who play both cricket and football also play volleyball
0.2(FV + FCV) = FCV
0.2FV = 0.8 FCV
20 members play both cricket and football
FV + FCV = 20
FCV = 4
We know that
- F + FV = 50
- C + CV \(\geq 30\)
F + FC + FV + FCV > C + FC + CV + FCV
F + FV > C + CV
Statement 1
(1) 40 percent of the members who play cricket and volleyball also play football.
0.4(CV + FCV) = FCV
4 = 0.4 (CV + FCV)
CV + FCV = 10
CV = 6
Hence, C > 24
Is F + FV > C + CV
Well, we can't say for sure. If CV = 25, C + CV < F + FV. However, if C = 100, C + CV > F + FV. The statement alone is not sufficient to answer the question. We can eliminate A and D.
Statement 2
(2) Number of members who play only cricket is less than half the number of members who play football.
Inference: C < 35
Is F + FV > C + CV
Well, we can't say for sure. If CV = 6, C + CV < F + FV. However, if CV = 50 & C = 34, C + CV > F + FV. The statement alone is not sufficient to answer the question. We can eliminate B.
Combined
We know that the value of CV = 6, and the max value of C = 34
Hence, at max C + CV = 40
Is F + FV > C + CV → Well, yes !
F + FV = 50, while maximum value of C + CV = 40. Hence, we can conclude that F + FV > C + CV
Option C
