AMC10 2004 A

AMC10 2004 A · Q7

AMC10 2004 A · Q7. It mainly tests Arithmetic misc, 3D geometry (volume).

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?

一个杂货商将橙子堆成金字塔状堆，矩形底面是 5 排橙子乘 8 排橙子。每层以上的橙子都搁在下面一层四个橙子形成的凹槽中。堆栈由一行橙子完成。堆栈中共有多少个橙子？

(A) 96 96

(B) 98 98

(D) 101 101

(E) 134 134

Answer

Correct choice: (C)

正确答案：（C）

Solution

There are five layers in the stack, and each of the top four layers has one less orange in its length and width than the layer on which it rests. Hence the total number of oranges in the stack is $5 \cdot 8 + 4 \cdot 7 + 3 \cdot 6 + 2 \cdot 5 + 1 \cdot 4 = 100$.

堆栈有五层，前四层每层的长宽比下面的层各少一个橙子。因此堆栈中橙子的总数是 $5 \cdot 8 + 4 \cdot 7 + 3 \cdot 6 + 2 \cdot 5 + 1 \cdot 4 = 100$。

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