Question 11

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Jambmaths question: 

In a youth club with 94 members, 60 like modern music and 50 like traditional music. The number of members who like both traditional and modern music is three times those who do not like any type of music. How many members like only one type of music?

Option A: 

8

Option B: 

24

Option C: 

62

Option D: 

86

Jamb Maths Solution: 

$\begin{align}  & n(\xi )=90 \\ & n(M)=60 \\ & n(T)=50 \\ & n{{(M\cup T)}^{1}}=x \\ & n(M\cap T)=3{{(M\cup T)}^{1}}=3x \\ & 94=60-3x+3x+50-3x+x \\ & 94=110-2x \\ & 16=2x \\ & x=8 \\ & \text{only Modern music }=n(M\cap {{T}^{1}})=60-3(8)=36 \\ & \text{only Traditional music}=n({{M}^{1}}\cap T)=50-3(8)=26 \\ & \text{Those who like just one music}=n(M\cap {{T}^{1}})+n({{M}^{1}}\cap T) \\ & \text{   }=36+26=62 \\\end{align}$

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