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# Qn 225. Club Number of students Chess 40 Drama 30 Math 25

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Manager
Joined: 28 Apr 2003
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Qn 225. Club Number of students Chess 40 Drama 30 Math 25 [#permalink]  20 Jan 2004, 05:06
Qn 225.

Club Number of students
Chess 40
Drama 30
Math 25

The table above shows the number of students in three clubs at McAuliffe School. Although no student is in all three clubs, 10 students are in both chess and drama, 5 students are in both chess and math, and 6 students are in both drama and math. How many different students are in the three clubs?

a. 68
b. 69
c. 74
d. 79
e. 84

I was wondering if the answer could be 25 + 14 + 14 [only students in chess club + only students in drama club + only students in math club] rather than 95 тАУ 21. [Total number of students тАУ 10+5+6].
Manager
Joined: 26 Dec 2003
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Yeah got 25+14+14=53 but its not in the choices
Senior Manager
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I think the answer complies with the basic forumlae for such questions:
P(A)+P(B)+P(C) - P(A+B) - P(B+C) -P(C+A) = P(A+B+C)

And I think this is the only we can find the unique( or in the jargon of the question..'different' ) number of students.

Vivek.
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"Start By Doing What Is Necessary ,Then What Is Possible & Suddenly You Will Realise That You Are Doing The Impossible"

Manager
Joined: 26 Dec 2003
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Location: India
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Confused abt the wording but if it was a real question and my choice 53 is not there I would add (10+5+6) only 2 of chess, drama and maths and arrive at 74 as the answer.
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