Jambmaths question:
In a school of 150 students, 80 offers french while 60 offers Arabic and 20 offer neither. How many students offer both subjects?
Option A:
45
Option B:
10
Option C:
35
Option D:
30
Jamb Maths Solution:
Let those that offer French be F, those that offer Arabic be A.In set denotation,$\begin{align} & n(\xi )=150 \\ & n(F)=80 \\ & n(A)=60 \\ & n(F\cup A)'=60 \\ & n(F\cap A)=x \\ & n(\xi )=n(F\cap A')+n(F\cap A)+n(F'\cap A)+n(F\cup A)' \\ & 150=(80-x)+x+(60-x)+20 \\ & 150=160-x \\ & x=10 \\ & n(F\cap A)=10 \\\end{align}$Those offering both subjects are 10
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