2007/08 AHSMC Part 1 Problem 2

Problem 2 of 16

Some cats have got into the pigeon loft because the total head count is $34$ but the total leg count is $80$ . The number of cats among the pigeons is

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Solution

Tell the cats to put their front legs up. Now there are still $34$ heads, but only $34 \times 2 = 68$ legs on the ground. Hence $80 - 68 = 12$ legs are up in the air, and each cat puts up $2$ of them. It follows that the number of cats is $12 \div 2 = 6$ . The answer is (A).

University of Alberta

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