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Venn Diagrams · Question 57 of 65

Question 57

MediumOriginal question

In a library survey, 42 members borrowed fiction, 36 borrowed biographies and 28 borrowed poetry. 14 borrowed fiction and biographies, 10 fiction and poetry, 12 biographies and poetry (each count includes those who borrowed all three), and 5 borrowed all three. How many members borrowed at least one of these?

Options for question 57

Show the answer and explanation
CorrectNot quiteAnswer C

Correct answer: C

Explanation

  1. Add the three totals: 42+36+28=10642 + 36 + 28 = 106.

  2. Subtract the pair counts: 106−36=70106 - 36 = 70.

  3. Add back all three: 70+5=7570 + 5 = 75.

Worth noting

70 stops before adding back the 5; 65 subtracts the 5 instead. 106 counts everyone who borrowed two or three kinds more than once.

Concept
Three-set inclusion–exclusion
Typical time
70 s
Your time
—
The rule this testsCounting with overlapping sets
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