Civil Services Examination · Question 68
There are three types of rectangular tiles: 3' × 3', 3' × 7' and 3' × 11'. An area of rectangular shape of dimensions 3' × 100' is to be covered using these tiles without breaking them. If x and y are the maximum and minimum numbers of tiles of various sizes, respectively, that can be used to cover the area exactly, then x - y is
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Answer: (A) 20
Explanation
Every tile spans the 3' width, so the lengths must sum to 100: 3a + 7b + 11c = 100. Maximum: 31 tiles of 3' + 1 of 7' = 32. Minimum: 8 of 11' + 4 of 3' = 12 (11 tiles is impossible by parity). x - y = 20.