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The color preferences of a group of girls were mapped and the results were as follows: 20 preferred pink, 16 preferred red and 14 preferred green. 5 preferred all the three colours. 9 of them chose Pink and Green. 7 of them chose Pink and Red. 8 of them chose Red and Green. How many girls chose only one colour?

The color preferences of a group of girls were mapped and the results were as follows: 20 preferred pink, 16 preferred red and 14 preferred green. 5 preferred all the three colours. 9 of them chose Pink and Green. 7 of them chose Pink and Red. 8 of them chose Red and Green. How many girls chose only one colour? Correct Answer 17

Given: 

20 preferred pink, 16 preferred red, and 14 preferred green.

5 preferred all three colours.

9 of them chose Pink and Green. 7 of them chose Pink and Red. 8 of them chose Red and Green. 

Concept used:

Venn Diagram

Calculation:

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So,

The number of girls who only chose Pink & Green = 9 - 5 =  4

The number of girls who only chose Pink & Red = 7 - 5 =  2

The number of girls who only chose Green & Red = 8 - 5 =  3

Now,

The number of girls who only chose Pink = 20 - 4 - 5 -2 = 9

The number of girls who only chose Red = 16 - 5 - 3 - 2= 6

The number of girls who only chose Green = 14 - 5 - 3 - 4 = 2

So, the number of girls who chose only one colour = (9 + 6 + 2) = 17

∴ 17 girls chose only one colour.

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