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
Detailed Explanation:
The area 3' × 100' must be covered by tiles 3' × 3', 3' × 7', and 3' × 11'. Since all tiles have width 3', they fit along the length, giving the equation 3a + 7b + 11c = 100.
Maximum tiles (x): Use smallest tiles. 31 tiles of 3' give 93', leaving 7' for 1 tile of 7'. Total = 32 tiles. Minimum tiles (y): Use largest tiles. 8 tiles of 11' give 88', leaving 12' for 4 tiles of 3'. Total = 12 tiles.
Therefore, x − y = 32 − 12 = 20, making Option 1 the correct answer.
Question 5 of 7 HCF and LCM
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