AMC8 2013

AMC8 2013 · Q6

AMC8 2013 · Q6. It mainly tests Linear equations, Fractions.

The number in each box below is the product of the numbers in the two boxes that touch it in the row above. For example, $30 = 6 \times 5$. What is the missing number in the top row?

下面每个盒子中的数字是它上方一行相邻两个盒子中数字的乘积。例如，$30 = 6 \times 5$。顶行缺失的数字是多少？

(A) 2 2

(B) 3 3

(D) 5 5

(E) 6 6

Answer

Correct choice: (C)

正确答案：（C）

Solution

Let the value in the empty box in the middle row be $x$, and the value in the empty box in the top row be $y$. $y$ is the answer we're looking for. From the diagram, $600 = 30x$, making $x = 20$. It follows that $20 = 5y$, so $y = \boxed{\textbf{(C)}\ 4}$.

设中间行空盒子的值为$x$，顶行空盒子的值为$y$。$y$是我们要找的答案。根据图示，$600 = 30x$，因此$x = 20$。进而，$20 = 5y$，所以$y = \boxed{\textbf{(C)}\ 4}$。

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