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Venn Diagrams · Question 56 of 65

Question 56

MediumOriginal question

At a sports camp, 15 children swim and cycle, 12 swim and skate, and 10 cycle and skate; these counts include the 6 children who do all three. How many children do at least two of the three activities?

19Correct answerYour answer25Correct answerYour answer31Correct answerYour answer37Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer B

Correct answer: B

Exactly two $= 15 + 12 + 10 - 3 \times 6 = 19$ .
At least two $= 19 + 6 = 25$ , which is $37 - 2 \times 6$ .

Worth noting

19 is exactly two and leaves out the 6 who do all three. 37 counts those 6 three times.

Concept: At least two = pair counts minus twice the centre
Typical timeTypical: 70 s
Your timeYours: —

The rule this testsCounting with overlapping sets

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