WAEC Mathematics 2014 Theory — Question 15
Question 15 of 23 from the West African Examinations Council (WAEC) Mathematics 2014 Theory paper, with the correct answer and a full explanation.
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9(a). In the Venn diagram, P, Q and R are subsets of the universal set U. If n(U)=125, find: (i) the value of x; (ii) n(P∩Q∩R′).
Model answer
Sum of all regions = 125: (16−2x)+5x+(6+x)+8x+4x+7x+(19−3x)+4 = 125 Constants: 16+6+19+4=45. x-terms: −2x+5x+x+8x+4x+7x−3x=20x 45+20x=125 ⟹ 20x=80 ⟹ x=4 (ii) n(P∩Q∩R′) = the region in both P and Q but not R = 5x = 5(4) = 20
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