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

[Vincen]

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

[Scott@TargetTestPrep]

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