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2004 AMC 12B Problem 8

Problem 8 of 25EasierAlgebra

A grocer makes a display of cans in which the top row has one can and each lower row has two more cans than the row above it. If the display contains 100100 cans, how many rows does it contain?

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Solution

The rows contain 1,3,5,…,(2n−1)1, 3, 5, \ldots, (2n - 1) cans, and the sum of the first nn odd numbers is n2.n^2. Setting n2=100n^2 = 100 gives n=10.n = 10. Thus, the correct answer is D.
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