AMC8 2013

AMC8 2013 · Q22

AMC8 2013 · Q22. It mainly tests Arithmetic misc, Area & perimeter.

Toothpicks are used to make a grid that is 60 toothpicks long and 32 toothpicks high. How many toothpicks are used altogether?

用牙签制作一个长 60 根牙签、高 32 根牙签的网格。总共用了多少根牙签？

(A) 1920 1920

(B) 1952 1952

(D) 2013 2013

(E) 3932 3932

Answer

Correct choice: (E)

正确答案：（E）

Solution

There are $61$ vertical columns with a length of $32$ toothpicks, and there are $33$ horizontal rows with a length of $60$ toothpicks, because $32$ and $60$ are the number of intervals. You can verify this by trying a smaller case, i.e. a $3 \times 4$ grid of toothpicks, with $3 \times 3$ and $2 \times 4$. Thus, our answer is $61\cdot 32 + 33 \cdot 60 = \boxed{\textbf{(E)}\ 3932}$.

有 61 条垂直线，每条长 32 根牙签，还有 33 条水平线，每条长 60 根牙签，因为 32 和 60 是间隔数。你可以用更小的例子验证，例如 $3 \times 4$ 牙签网格，有 $3 \times 3$ 和 $2 \times 4$。因此，总数是 $61\cdot 32 + 33 \cdot 60 = \boxed{\textbf{(E)}\ 3932}$。

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