2004 AMC 12B Problem 8

Attempt Problem 8 of the 2004 AMC 12B below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2004 AMC 12B solutions, or check the answer key.

All problems are used with official legal permission of the Mathematical Association of America (MAA).

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?

5

8

9

10

11

The row counts are

1, 3, 5, \ldots,

the odd numbers

The sum of the first

n

odd numbers is

n^2

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.

Problem 8 in other years