Using the diagram of Class 12 activities, find how many students of Class 12 do not 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.

Using the diagram of Class 12 activities, find…

Using the diagram of Class 12 activities, find how many students of Class 12 do not paint.

Question 39

HardOriginal question

Using the diagram of Class 12 activities, find how many students of Class 12 do not 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.

25Correct answerYour answer32Correct answerYour answer44Correct answerYour answer57Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer B

Correct answer: B

Class 12 has $11 + 8 + 13 + 6 + 4 + 5 + 3 + 7 = 57$ students.
Painters $= 13 + 4 + 5 + 3 = 25$ .
Students who do not paint $= 57 - 25 = 32$ . (Check: $11 + 8 + 6 + 7 = 32$ .)

Worth noting

25 is the number of painters, and also what you get if you forget the 7 students outside every circle $(11 + 8 + 6)$ . 44 subtracts only the Only Painters region $(57 - 13)$ . 57 is the whole class.

Concept: Complement of a set inside the universe
Typical timeTypical: 120 s
Your timeYours: —

The rule this testsReading a labelled diagram

Practise this chapter →

Ten questions from Venn Diagrams, at your own pace.

Practise this chapter →

Ten questions from Venn Diagrams, at your own pace.

Using the diagram of Class 12 activities, find how many students of Class 12 do not paint.

Question 39

Explanation