The diagram shows which students of Class 12 dance, sing or paint. How many students sing but neither dance nor paint? Venn diagram of three overlapping circles labelled Dancers, Singers and Painters inside a box labelled Students in Class 12. Only Dancers: 11. Only Singers: 8. Only Painters: 13. Dancers and Singers only: 6. Dancers and Painters only: 4. Singers and Painters only: 5. All three: 3. Outside all three: 7.

The diagram shows which students of Class 12…

The diagram shows which students of Class 12 dance, sing or paint.

EasyOriginal question

The diagram shows which students of Class 12 dance, sing or paint. How many students sing but neither dance nor paint?

8Correct answerYour answer13Correct answerYour answer14Correct answerYour answer22Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer A

Correct answer: A

'Sing but neither dance nor paint' is the part of Singers outside both other circles: the Only Singers region.
That region shows 8.

Worth noting

22 is the whole Singers circle $(8 + 6 + 5 + 3)$ ; 13 and 14 keep one shared region by mistake. The word 'neither' leaves only the unshared part.

Ten questions from Venn Diagrams, at your own pace.

Ten questions from Venn Diagrams, at your own pace.