In a group the numbers in the three outer parts are in the ratio 2 : 3 : 4 (2k, 3k and 4k), and 90 people are in exactly one circle. How many people are in circle C?

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Accepted Answer

60. Exactly one: 2k + 3k + 4k = 9k = 90, so k = 10 and C only = 40. Circle C = 40 + 6 + 9 + 5 = 60. 40 is C only, 55 forgets the 5 in the centre, and 67 wrongly adds the 7 that lies outside C.

In a group the numbers in the three outer parts are in the ratio 2 : 3 : 4 (2k, 3k and 4k), and 90 people are in exactly one circle. How many people are in circle C?

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