In a class of 50 students, 20 play Hockey, 15 play Cricket and 11 play Football. 7 play both Hockey and Cricket, 4 play

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Vincen: Legendary Member; Posts: 2898; Joined: Thu Sep 07, 2017 2:49 pm; Thanked: 6 times; Followed by:5 members

In a class of 50 students, 20 play Hockey, 15 play Cricket and 11 play Football. 7 play both Hockey and Cricket, 4 play

by Vincen » Tue Jan 19, 2021 9:39 am

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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

Answer: B

Source: Manhattan GMAT

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Source: Beat The GMAT — Problem Solving | Tue Jan 19, 2021 9:39 am

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8086; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

Re: In a class of 50 students, 20 play Hockey, 15 play Cricket and 11 play Football. 7 play both Hockey and Cricket, 4 p

by Scott@TargetTestPrep » Sun Jan 24, 2021 5:39 am

Vincen wrote: ↑
Tue Jan 19, 2021 9:39 am
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

Answer: B

Solution:

Since 18 students do not play any of the three sports, then 50 - 18 = 32 students must play at least one of the 3 sports. This total can be formulated as follows:

Total = #(H) + #(C) + #(F) - #(H and C) - #(C and F) - #(H and F) + #(H and C and F)

Thus, we have:

32 = 20 + 15 + 11 - 7 - 4 - 5 + #(H and C and F)

32 = 30 + #(H and C and F)

2 = #(H and C and F)

Since #(H and C) = 7 (which also include those who play Football), but we’ve found that #(H and C and F) = 2, there must be 7 - 2 = 5 students who play Hockey and Cricket only. Similarly, there must be 4 - 2 = 2 students who play Cricket and Football only, and 5 - 2 = 3 students who play Hockey and Football only. Thus, there must be 5 + 2 + 3 = 10 students who play exactly 2 sports.

Answer: B

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