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# In a group of 68 students, each student is registered for at least one

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Intern
Joined: 02 Nov 2009
Posts: 19
Schools: Saïd (R3) - Admitted
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In a group of 68 students, each student is registered for at least one [#permalink]

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05 Dec 2009, 07:14
2
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Difficulty:

25% (medium)

Question Stats:

68% (01:56) correct 32% (01:01) wrong based on 137 sessions

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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

[Reveal] Spoiler:
I just want to understand why this question cannot be solved by using equation

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

OPEN DISCUSSION OF THIS QUESTION IS HERE: in-a-group-of-68-students-each-student-is-registered-for-at-106500.html
[Reveal] Spoiler: OA
VP
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Posts: 1473
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Re: In a group of 68 students, each student is registered for at least one [#permalink]

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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
Intern
Joined: 17 Nov 2009
Posts: 37
Schools: University of Toronto, Mcgill, Queens
Followers: 0

Kudos [?]: 88 [0], given: 9

Re: In a group of 68 students, each student is registered for at least one [#permalink]

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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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VP
Joined: 05 Mar 2008
Posts: 1473
Followers: 11

Kudos [?]: 258 [0], given: 31

Re: In a group of 68 students, each student is registered for at least one [#permalink]

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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
Intern
Joined: 17 Nov 2009
Posts: 37
Schools: University of Toronto, Mcgill, Queens
Followers: 0

Kudos [?]: 88 [0], given: 9

Re: In a group of 68 students, each student is registered for at least one [#permalink]

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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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Joined: 16 Nov 2010
Posts: 1673
Location: United States (IN)
Concentration: Strategy, Technology
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Kudos [?]: 492 [0], given: 36

Re: In a group of 68 students, each student is registered for at least one [#permalink]

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16 May 2011, 05:27
mgmat-cat-3-overlapping-sets-106500.html
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Re: In a group of 68 students, each student is registered for at least one [#permalink]

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14 Dec 2014, 11:10
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

use this
Total = Group 1 + Group 2 + Group 3 - (people in 2 groups) - 2(people in all 3 groups) + none.
Math Expert
Joined: 02 Sep 2009
Posts: 35327
Followers: 6649

Kudos [?]: 85884 [1] , given: 10260

Re: In a group of 68 students, each student is registered for at least one [#permalink]

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15 Dec 2014, 07:29
1
This post received
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sinharavi wrote:
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

[Reveal] Spoiler:
I just want to understand why this question cannot be solved by using equation

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

"Each student is registered for at least one of three classes" means that there are no students who are registered for none of the classes.

Total = {people in group A} + {people in group B} + {people in group C} - {people in exactly 2 groups} - 2*{people in exactly 3 groups} + {people in none of the groups}:

68 = 25 + 25 + 34 - {people in exactly 2 groups} - 2*3 + 0 --> {people in exactly 2 groups}=10

Answer: B.

Look at the diagram:

We need to find {people in exactly 2 groups}, so yellow section. Now, when we sum {people in group A} + {people in group B} + {people in group C} we count students who are in exactly 2 groups (yellow section) twice, so to get rid of double counting we are subtracting {people in exactly 2 groups} once.

Similarly when we sum {people in group A} + {people in group B} + {people in group C} we count students who are in exactly 3 groups (blue section) thrice (as it is the portion of all three groups), so to count this group only once we are subtracting 2*{people in exactly 3 groups}.

For more on this check: formulae-for-3-overlapping-sets-69014.html#p729340

OPEN DISCUSSION OF THIS QUESTION IS HERE: in-a-group-of-68-students-each-student-is-registered-for-at-106500.html
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Re: In a group of 68 students, each student is registered for at least one   [#permalink] 15 Dec 2014, 07:29
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# In a group of 68 students, each student is registered for at least one

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