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Of the 32 students in a certain class, 15 are in a music club and 20 01 Nov 2015, 02:11
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Of the 32 students in a certain class, 15 are in a music club and 20 are in a dance club. If 10 of the students are not in either club, how many of the students are in only one of the two clubs?

A. 5
B. 9
C. 10
D. 17
E. 25
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B
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Of the 32 students in a certain class, 15 are in a music club and 20 01 Nov 2015, 06:15
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We can solve this question using the double matrix method( The values in black are given while the ones in blue have been calculated)

Number of students in only one of the 2 clubs = (Number of students in Music and Dance') + (Number of students in Dance and Music')
=2+7=9
Answer B
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Of the 32 students in a certain class, 15 are in a music club and 20 01 Nov 2015, 03:47
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Bunuel
Of the 32 students in a certain class, 15 are in a music club and 20 are in a dance club. If 10 of the students are not in either club, how many of the students are in only one of the two clubs?

A. 5
B. 9
C. 10
D. 17
E. 25
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Easiest way is to make a table:


M M' Total
D 13 7 20
D' 2 10 12
Total 15 17 32

7+2=9 students

Answer: B
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Of the 32 students in a certain class, 15 are in a music club and 20 01 Nov 2015, 05:41
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Venn Diagram can solve this prob:
Let the number of pupils who play in both music and dance be x.
Number of pupils who play music only + Pupils in Dance only + Pupils in both dance and music + Pupils in none of the 2 = 32
(15-x)+x+(20-x) = 32
x= 13
Number of Pupils who play music only= 15-13=2
Number of Pupils who is in dance only = 20-13=7
Number of Pupils in only one club= 7+2 =9

Ans: B
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Of the 32 students in a certain class, 15 are in a music club and 20 01 Nov 2015, 06:03
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Out of 32
10 are not in either of the clubs

Thus

22 = 15 + 20 -both

Both = 13

Therefore

only music = 15-13 = 2
only Dance = 20 - 13 = 7

Hence 7 + 2 =9
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Of the 32 students in a certain class, 15 are in a music club and 20 02 Nov 2015, 04:55
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skywalker18
We can solve this question using the double matrix method( The values in black are given while the ones in blue have been calculated)

Number of students in only one of the 2 clubs = (Number of students in Music and Dance') + (Number of students in Dance and Music')
=2+7=9
Answer B
Show more

Hi, skywalker18, would you pls clarify the formula? What's the meaning of Music Club & Music Club`? Again how will we know that 10 will be put in that grid?

Thanks in advance.
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Of the 32 students in a certain class, 15 are in a music club and 20 02 Nov 2015, 05:00
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Hi suravi,

Hope skywalker wont mind i am answering on behalf of him.:p

Music=those students in music club
music'=those students not in music club
so dance'=those students who are not in dance.

In the qns,it was stated 10pupils are in neither of the club. Thus 10 is placed in the region of music' and dance'
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Of the 32 students in a certain class, 15 are in a music club and 20 02 Nov 2015, 06:55
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suravi
skywalker18
We can solve this question using the double matrix method( The values in black are given while the ones in blue have been calculated)

Number of students in only one of the 2 clubs = (Number of students in Music and Dance') + (Number of students in Dance and Music')
=2+7=9
Answer B

Hi, skywalker18, would you pls clarify the formula? What's the meaning of Music Club & Music Club`? Again how will we know that 10 will be put in that grid?

Thanks in advance.
Show more

suravi
Music club' is the complement of Music club . 10 students are not in either Music or Dance club has been stated in the question.
wahaha has explained the rest .

Hope it helps !! :)
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Of the 32 students in a certain class, 15 are in a music club and 20 05 Nov 2015, 00:31
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@wahaba & skywalker18

Lots of thanks. Initially it was not easy, now at got the operation :)
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Of the 32 students in a certain class, 15 are in a music club and 20 28 Mar 2025, 20:37
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Of the 32 students in a certain class, 15 are in a music club and 20 11 Apr 2025, 11:53
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I'm confused as to when do we use the A+B-BOTH+EITHER = N, AUB = A + B - AUNIONB , OR DOUBLESET MATRIX
Skywalker18
We can solve this question using the double matrix method( The values in black are given while the ones in blue have been calculated)

Number of students in only one of the 2 clubs = (Number of students in Music and Dance') + (Number of students in Dance and Music')
=2+7=9
Answer B
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