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2020 AMC 10A Question 3

AMC10 · 2020 AMC 10A

Question 3

Assuming $a\neq3,$ $b\neq4,$ and $c\neq5,$ what is the value in simplest form of the following expression? $$
\frac{a-3}{5-c} \cdot \frac{b-4}{3-a} \cdot \frac{c-5}{4-b}
$$
  1. $-1$
  2. $1$
  3. $\displaystyle \frac{abc}{60} $
  4. $\displaystyle \frac{1}{abc} - \frac{1}{60}$
  5. $\displaystyle \frac{1}{60} - \frac{1}{abc}$