2020 AMC 10A Problem 3

Name: 2020 AMC 10A Problem 3 — Video Solution
Uploaded: 2022-11-05T14:22:22-07:00
Duration: 2 h 28 min 50 s
Description: Po-Shen Loh presents the video solution to 2020 AMC 10A Problem 3, from "2020 AMC 10A LIVE Solve".

Question

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}

Answer: A

Concepts:algebraic manipulation fraction

Difficulty rating: 770

Small hint:

Each denominator is the negative of a matching numerator factor

Big hint:

Count the number of negative signs after cancellation

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.