2004 AMC 10A Problem 7

Below is the professionally curated solution for Problem 7 of the 2004 AMC 10A, from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2004 AMC 10A solutions, or check the answer key.

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Concepts:basic counting summation

Difficulty rating: 1100

A grocer stacks oranges in a pyramid-like stack whose rectangular base is $5$ oranges by $8$ oranges. Each orange above the first level rests in a pocket formed by four oranges in the level below. The stack is completed by a single row of oranges. How many oranges are in the stack?

$96$

$98$

$100$

$101$

$134$

Solution:

There are five layers, each one shorter and narrower than the one below. The total number of oranges is $5\cdot 8 + 4\cdot 7 + 3\cdot 6 + 2\cdot 5 + 1\cdot 4 = 40 + 28 + 18 + 10 + 4 = 100.$

Thus, the correct answer is C.

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