In a youth club with 94 members, 60 like modern music, and 50 like traditional music. The number who like both is three times those who like neither. How many members like only one type of music?

Question 463 of 480

In a youth club with 94 members, 60 like modern music, and 50 like traditional music. The number who like both is three times those who like neither. How many members like only one type of music?

Correct Answer: C

Explanation

Let n = number who like neither. Let b = number who like both. Then b = 3n. Using the principle: Total = Modern + Traditional - Both + Neither. 94 = 60 + 50 - b + n. Substituting b = 3n: 94 = 110 - 3n + n → 94 = 110 - 2n → 2n = 16 → n = 8, b = 24. Only one type = (Modern only) + (Traditional only) = (60-24) + (50-24) = 36 + 26 = 62.