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Venn Diagrams · Question 50 of 65

Question 50

MediumOriginal question

In a housing society, 14 families own both a car and a scooter, 11 own both a car and a bicycle, and 9 own both a scooter and a bicycle. These counts include the 4 families that own all three. How many families own exactly two of the three?

Options for question 50

Show the answer and explanation
CorrectNot quiteAnswer A

Correct answer: A

Explanation

  1. Each pair count contains the 4 all-three families, so remove them from each: 10,7,510, 7, 5.

  2. Exactly two =10+7+5=22= 10 + 7 + 5 = 22, which is 34−3×434 - 3 \times 4.

Worth noting

30 removes the 4 only once and 26 removes it twice. The all-three families sit inside all three pair counts, so they must go three times.

Concept
Exactly two equals the pair counts minus three times the centre
Typical time
70 s
Your time
—
The rule this testsCounting with overlapping sets
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