Question

一位杂货商把橙子堆成类似金字塔的形状，长方形底层为 $5$ 个橙子乘 $8$ 个橙子。第一层以上的每个橙子都放在下一层四个橙子形成的凹处。最上层是一排橙子。这个橙子堆共有多少个橙子？

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?

$96$

$98$

$100$

$101$

$134$

答案：C

知识点：基本计数求和

难度评级：1100

解答：

共有五层，每层都比下面一层少一行且少一列。 $\begin{aligned} &5\cdot 8 + 4\cdot 7 + 3\cdot 6 \\ &\quad {}+ 2\cdot 5 + 1\cdot 4 \\ &= 40 + 28 + 18 + 10 + 4 = 100. \end{aligned}$

所以正确答案是 C。

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

Thus, the correct answer is C.

2004 AMC 10A 第 7 题

答案：C

难度评级：1100

解答：

其他年份的第 7 题