2004 AMC 10A Problems/Problem 7

Revision as of 17:34, 4 November 2006 by B-flat (talk | contribs)
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)

Problem

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 below. The stack is completed by a single row of oranges. How many oranges are in the stack?

$\mathrm{(A) \ } 96 \qquad \mathrm{(B) \ } 98 \qquad \mathrm{(C) \ } 100 \qquad \mathrm{(D) \ } 101 {2}\qquad \mathrm{(E) \ } 134$

Solution

There are $5\times8=40$ oranges on the 1st layer of the stack. When the 2nd layer is added on top of the first, it will be a layer of $4\times7=28$ oranges. When the third layer is added on top of the 2nd, it will be a layer of $3\times6=18$ oranges, etc.

Therefore, there are $5\times8+4\times7+3\times6+2\times5+1\times4=40+28+18+10+4=100$ oranges in the stack $\Rightarrow\mathrm{(C)}$.

See Also

Invalid username
Login to AoPS