Each of the 104 employees of a company attends at least one of the yoga, Zumba and aerobics classes. 50 attend yoga, 45 Zumba and 40 aerobics; 15 attend both yoga and Zumba, 12 both yoga and aerobics, and 10 both Zumba and aerobics (each of these counts includes those who attend all three). How many employees attend exactly one class?

67Correct answerYour answer73Correct answerYour answer79Correct answerYour answer85Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer C

Correct answer: C

All three: $104 = 50 + 45 + 40 - 15 - 12 - 10 + x$ , so $104 = 98 + x$ and $x = 6$ .
Exactly two $= 15 + 12 + 10 - 3 \times 6 = 19$ .
Exactly one $= 104 - 19 - 6 = 79$ .

Worth noting

67 subtracts the raw pair counts (37). 85 forgets to remove the 6 who attend all three. 73 removes the centre only twice from the pair counts.

Ten questions from Venn Diagrams, at your own pace.

Explanation