In a class of 50 students, 20 play Hockey, 15 play Cricket

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In a class of 50 students, 20 play Hockey, 15 play Cricket [#permalink]

01 May 2012, 21:28

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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

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Re: In a class of 50 students, 20 play Hockey, 15 play Cricket [#permalink]

01 May 2012, 23:27

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gmihir wrote:

Notice that "7 play both Hockey and Cricket" does not mean that out of those 7, some does not play Football too. The same for Cricket/Football and Hockey/Football.

{Total}={Hockey}+{Cricket}+{Football}-{HC+CH+HF}+{All three}+{Neither} For more check ADVANCED OVERLAPPING SETS PROBLEMS

50=20+15+11-(7+4+5)+{All three}+18 --> {All three}=2;

Those who play ONLY Hockey and Cricket are 7-2=5;
Those who play ONLY Cricket and Football are 4-2=2;
Those who play ONLY Hockey and Football are 5-2=3;

Hence, 5+2+3=10 students play exactly two of these sports.

Answer: B.
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Joined: 11 Jul 2012

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Re: In a class of 50 students, 20 play Hockey, 15 play Cricket [#permalink]

09 Oct 2012, 11:39

I don't agree with the answer given
If the question is correctly worded the answer ought to be 7 + 5 + 4 = 16
But if the question is: How many students play exactly one of these sports then the answer could be 10 (I haven't checked)
Brother Karamazov

Re: In a class of 50 students, 20 play Hockey, 15 play Cricket [#permalink] 09 Oct 2012, 11:39

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In a class of 50 students, 20 play Hockey, 15 play Cricket

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In a class of 50 students, 20 play Hockey, 15 play Cricket

In a class of 50 students, 20 play Hockey, 15 play Cricket

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