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GRE Prep Club Team Member
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Posts: 2960
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In a class of 50 students, 20 play Hockey, 15 play Cricket and 11 play
[#permalink]
23 Mar 2021, 05:00
23 Mar 2021, 05:00
Expert Reply
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Question Stats:
52% (02:29) correct
47% (03:18) wrong based on 59 sessions
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In a class of 50 students, 20 play Hockey, 15 play Cricket and 11 play Football. 7 play both Hockey and Cricket, 4 play Cricket and Football and 5 play Hockey and football. If 18 students do not play any of these given sports, how many students play exactly two of these sports?
A. 12
B. 10
C. 11
D. 15
E. 14
A. 12
B. 10
C. 11
D. 15
E. 14
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Joined: 16 Apr 2020
Status:Founder & Quant Trainer
Affiliations: Prepster Education
Posts: 1546
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WE:Education (Education)
Re: In a class of 50 students, 20 play Hockey, 15 play Cricket and 11 play
[#permalink]
23 Mar 2021, 09:05
23 Mar 2021, 09:05
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2
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GeminiHeat wrote:
In a class of 50 students, 20 play Hockey, 15 play Cricket and 11 play Football. 7 play both Hockey and Cricket, 4 play Cricket and Football and 5 play Hockey and football. If 18 students do not play any of these given sports, how many students play exactly two of these sports?
A. 12
B. 10
C. 11
D. 15
E. 14
A. 12
B. 10
C. 11
D. 15
E. 14
Total - Leftovers = H + C + F - (H∩C) - (C∩F) - (H∩F) + (H∩C∩F)
50 - 18 = 20 + 15 + 11 - 7 - 4 - 5 + (H∩C∩F)
(H∩C∩F) = 2
Only (H∩C) = 7 - 2 = 5
Only (C∩F) = 4 - 2 = 2
Only (H∩F) = 5 - 2 = 3
So, students playing exactly two sports = 5 + 2 + 3 = 10
Hence, option B
General Discussion
Re: In a class of 50 students, 20 play Hockey, 15 play Cricket and 11 play
[#permalink]
28 Jul 2026, 16:12
28 Jul 2026, 16:12
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Thanks to another GRE Prep Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).
Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
