Past papers › JAMB 2000 · UME › Question 4 Question JAMB General Maths 2000 Objective Sets & Venn diagrams Sets & Venn diagrams
In a youth club with 94 members, 60 like modern music and 50 like traditional music. The number of members who like both is three times the number who like neither. How many members like only one type of music?
Worked solution (try it first) Let
n n n members like neither, so
3 n 3n 3 n like both.
Members who like at least one:
60 + 50 − 3 n = 94 − n 60 + 50 - 3n = 94 - n 60 + 50 − 3 n = 94 − n .
So
110 − 3 n = 94 − n 110 - 3n = 94 - n 110 − 3 n = 94 − n , which gives
2 n = 16 2n = 16 2 n = 16 and
n = 8 n = 8 n = 8 .
So 24 like both.
Modern only:
60 − 24 = 36 60 - 24 = 36 60 − 24 = 36 .
Traditional only:
50 − 24 = 26 50 - 24 = 26 50 − 24 = 26 .
Only one type:
36 + 26 = 62 36 + 26 = 62 36 + 26 = 62 , option C.
Watch out
"Only one type" leaves out both the 8 who like neither and the 24 who like both. 94 − 8 = 86 94 - 8 = 86 94 − 8 = 86 Report a problem with this question