2014/15 AHSMC Part 1 Problem 16
Problem 16 of 16
Four cages are arranged in a formation. Each cage contains some chickens and some rabbits (some cages may contain only chickens or only rabbits). The total number of heads in the two cages in the first row is . The total number of legs in the two cages in the second row is . The total number of heads in the two cages in the first column is . The total number of legs in the two cages in the second column is . The minimum number of animals in all four cages is
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Solution
There are legs in the two cages in the second column. Since , they may come from as few as animals, namely, rabbits and chicken. Hence the minimum number of animals in all four cages is . If we have animals in the first cage in the first row, chickens and rabbits in the second cage in the first row, chickens and rabbits in the first cage in the second row, and chicken and rabbits in the second cage in the second row, we have animals overall. The answer is (B).