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Venn Diagrams · Question 65 of 65

Question 65

HardOriginal question

In a group of 72 friends, 12 like neither tea nor coffee. The number who like only tea is three times the number who like both, and the number who like only coffee is twice the number who like both. How many like tea?

Options for question 65

Show the answer and explanation
CorrectNot quiteAnswer D

Correct answer: D

Explanation

  1. Let xx like both. Then only tea =3x= 3x and only coffee =2x= 2x.

  2. 3x+2x+x=72−12=603x + 2x + x = 72 - 12 = 60, so x=10x = 10.

  3. Tea drinkers =3x+x=40= 3x + x = 40.

Worth noting

30 is only tea; everyone who likes both also likes tea. 20 is only coffee and 10 is both.

Concept
Setting up regions with a variable
Typical time
120 s
Your time
—
The rule this testsCounting with overlapping sets
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