Mechmeera wrote:In the floor of a particular kitchen owned by an abstract artist, each row of tiles to the right of the first row contains two fewer tiles than the row directly to its left. If there are nine rows in all and a total of 504 tiles in the floor, how many tiles does the left-most row contain?
(A) 52
(B) 56
(C) 60
(D) 64
(E) 68
Since each row contains 2 fewer tiles than the row directly to its left, the 9 rows constitute an EVENLY SPACED SET.
For any evenly spaced set, average = median = sum/number.
Thus, the length of the center row = the median length of the 9 rows = (total number of tiles)/(total number of rows) = 504/9 = 56.
Since there are 4 rows to the left of the center row, and each successive row to the left increases by a length of 2 tiles, the length of the leftmost row = 56 + 4*2 = 64.
The correct answer is
D.
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