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In a group of 68 students, each student is registered for at least one [#permalink]
05 Dec 2009, 06:14

00:00

A

B

C

D

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Difficulty:

25% (medium)

Question Stats:

76% (02:11) correct
24% (01:09) wrong based on 75 sessions

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?

Re: In a group of 68 students, each student is registered for at least one [#permalink]
05 Dec 2009, 06:41

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

Re: In a group of 68 students, each student is registered for at least one [#permalink]
05 Dec 2009, 10:09

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.

Re: In a group of 68 students, each student is registered for at least one [#permalink]
05 Dec 2009, 13:53

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.

Re: In a group of 68 students, each student is registered for at least one [#permalink]
05 Dec 2009, 23:53

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.

Re: In a group of 68 students, each student is registered for at least one [#permalink]
14 Dec 2014, 10:10

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.

Re: In a group of 68 students, each student is registered for at least one [#permalink]
15 Dec 2014, 06:29

Expert's post

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?

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}:

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}.

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