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

100

cans, how many rows does it contain?

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Solution

The rows contain

1, 3, 5, \ldots, (2n - 1)

cans, and the sum of the first

n

odd numbers is

n^2.

Setting

n^2 = 100

gives

n = 10.

Thus, the correct answer is D.

Concepts: sum of first n odd numbers

Problem text and solution from the LIVE past-contest archive. See also the AoPS wiki page for community solutions.