In a class of 46, 18 students take Art but not Music, 12 take Music but not Art, and 10 take both. How many take neither subject?

6Correct answerYour answer16Correct answerYour answer26Correct answerYour answer40Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer A

Correct answer: A

The three numbers given are separate regions (Art only, Music only, both), so simply add them: $18 + 12 + 10 = 40$ .
Neither $= 46 - 40 = 6$ .

Worth noting

16 forgets the 10 who take both. 26 subtracts the 10 as if the first two numbers already contained it; 'but not' tells you they do not.

Ten questions from Venn Diagrams, at your own pace.

Explanation