Statement: In a survey of the households of a residential colony, 70 per cent reported owning at least one bicycle and 40 per cent reported owning at least one car. Conclusions: I. At least 10 per cent of the households own both a bicycle and a car. II. No household in the colony is without a vehicle. Which of the conclusions follows from the statement?

Question

Accepted Answer

Only conclusion I follows. The two figures add up to 110 per cent of the same set of households, so the overlap must be at least 110 − 100 = 10 per cent; I follows. The 30 per cent without a bicycle need not all own cars, so some households may own nothing at all — II does not follow.

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