2020 AMC 10A Problem 3

Below is the video solution and professionally curated solution for Problem 3 of the 2020 AMC 10A, from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2020 AMC 10A solutions, or check the answer key.

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Concepts:algebraic manipulation fraction

Difficulty rating: 770

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

$-1$

$1$

$\displaystyle \frac{abc}{60}$

$\displaystyle \frac{1}{abc} - \frac{1}{60}$

$\displaystyle \frac{1}{60} - \frac{1}{abc}$

Video solution:

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Written solution:

Rewrite the denominator factors as $5-c=-(c-5)$ , $3-a=-(a-3)$ , and $4-b=-(b-4)$ . The expression becomes $\dfrac{(a-3)(b-4)(c-5)}{-(a-3)(b-4)(c-5)}=-1$ . Thus, A is the correct answer.

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