AMC10 2020 A

AMC10 2020 A · Q3

AMC10 2020 A · Q3. It mainly tests Manipulating equations.

Assuming $a \neq 3$, $b \neq 4$, and $c \neq 5$, what is the value in simplest form of the following expression? $\frac{a-3}{5-c} \cdot \frac{b-4}{3-a} \cdot \frac{c-5}{4-b}$

假设$a \neq 3$，$b \neq 4$，$c \neq 5$，下式的最简形式的值是多少？$\frac{a-3}{5-c} \cdot \frac{b-4}{3-a} \cdot \frac{c-5}{4-b}$

(A) -1 -1

(B) 1 1

(D) $\frac{1}{abc - 60}$ $\frac{1}{abc - 60}$

(E) $\frac{1}{60 - abc}$ $\frac{1}{60 - abc}$

Answer

Correct choice: (A)

正确答案：（A）

Solution

Because $\frac{x-y}{y-x} = \frac{x-y}{-(x-y)} = -1$, the expression simplifies to $\frac{a-3}{5-a} \cdot \frac{b-4}{4-b} \cdot \frac{c-5}{5-c} = (-1)^3 = -1$.

因为$\frac{x-y}{y-x} = \frac{x-y}{-(x-y)} = -1$，所以原式简化为$\frac{a-3}{5-a} \cdot \frac{b-4}{4-b} \cdot \frac{c-5}{5-c} = (-1)^3 = -1$。

Topics

AL.016 Manipulating equations