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In a group of 68 students

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In a group of 68 students [#permalink] New post 05 Dec 2009, 07:14
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Question Stats:

50% (02:07) correct 50% (01:14) wrong based on 2 sessions
This is a question from one of MGMAT tests.

In a group of 68 students, each student is registered for at least one of three classes – History, Math and English. Twenty-five students are registered for History, twenty-five students are registered for Math, and thirty-four students are registered for English. If only three students are registered for all three classes, how many students are registered for exactly two classes?

A. 13

B. 10

C. 9

D. 8

E. 7




I just want to understand why this question cannot be solved by using equation

AUBUC = A + B +C - AintB - BintC - CintA + AintBintC
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Re: In a group of 68 students [#permalink] New post 05 Dec 2009, 07:41
sinharavi wrote:
This is a question from one of MGMAT tests.

In a group of 68 students, each student is registered for at least one of three classes – History, Math and English. Twenty-five students are registered for History, twenty-five students are registered for Math, and thirty-four students are registered for English. If only three students are registered for all three classes, how many students are registered for exactly two classes?

A. 13

B. 10

C. 9

D. 8

E. 7




I just want to understand why this question cannot be solved by using equation

AUBUC = A + B +C - AintB - BintC - CintA + AintBintC


no need to repeat this post

formulae-for-3-overlapping-sets-69014.html
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Schools: University of Toronto, Mcgill, Queens
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Re: In a group of 68 students [#permalink] New post 05 Dec 2009, 11:09
sinharavi wrote:
This is a question from one of MGMAT tests.

In a group of 68 students, each student is registered for at least one of three classes – History, Math and English. Twenty-five students are registered for History, twenty-five students are registered for Math, and thirty-four students are registered for English. If only three students are registered for all three classes, how many students are registered for exactly two classes?

A. 13

B. 10

C. 9

D. 8

E. 7




I just want to understand why this question cannot be solved by using equation

AUBUC = A + B +C - AintB - BintC - CintA + AintBintC


The above equation will result is 22 however the question asks for exactly two classes.

P(AnB) + P(AnC) + P(BnC) - 3P(AnBnC)
= 22- 3(3) = 22 - 9 = 13

What is the OA?
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Re: In a group of 68 students [#permalink] New post 05 Dec 2009, 14:53
Bullet wrote:
sinharavi wrote:
This is a question from one of MGMAT tests.

In a group of 68 students, each student is registered for at least one of three classes – History, Math and English. Twenty-five students are registered for History, twenty-five students are registered for Math, and thirty-four students are registered for English. If only three students are registered for all three classes, how many students are registered for exactly two classes?

A. 13

B. 10

C. 9

D. 8

E. 7




I just want to understand why this question cannot be solved by using equation

AUBUC = A + B +C - AintB - BintC - CintA + AintBintC


The above equation will result is 22 however the question asks for exactly two classes.

P(AnB) + P(AnC) + P(BnC) - 3P(AnBnC)
= 22- 3(3) = 22 - 9 = 13

What is the OA?


answer should be 10

12 History
22 Math
21 English
3 in all three
10 in both
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Re: In a group of 68 students [#permalink] New post 06 Dec 2009, 00:53
Bullet wrote:
sinharavi wrote:
This is a question from one of MGMAT tests.

In a group of 68 students, each student is registered for at least one of three classes – History, Math and English. Twenty-five students are registered for History, twenty-five students are registered for Math, and thirty-four students are registered for English. If only three students are registered for all three classes, how many students are registered for exactly two classes?

A. 13

B. 10

C. 9

D. 8

E. 7




I just want to understand why this question cannot be solved by using equation

AUBUC = A + B +C - AintB - BintC - CintA + AintBintC


The above equation will result is 22 however the question asks for exactly two classes.

P(AnB) + P(AnC) + P(BnC) - 3P(AnBnC)
= 22- 3(3) = 22 - 9 = 13

What is the OA?


My Apologies, that my upper post has tyoe. I don't know how it happen

P(A u B u C) = P(A) + P(B) + P(C) – P(A n B) – P(A n C) – P(B n C) + P(A n B n C)
68 = 25+ 25+ 34 - P(A n B) – P(A n C) – P(B n C) + 3

P(A n B) + P(A n C) + P(B n C) = 19

for exactly two persons we need to find out.

P(A n B) + P(A n C) + P(B n C) – 3P(A n B n C)
= 19 - 3(3) = 10
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Re: In a group of 68 students [#permalink] New post 16 May 2011, 05:27
mgmat-cat-3-overlapping-sets-106500.html
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Re: In a group of 68 students   [#permalink] 16 May 2011, 05:27
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