2020 AMC 10 A

Complete problem set with solutions and individual problem pages

Problem 3 Easy

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}

(2020 AMC 10A Problems, Question #3)

  • A.

    -1

  • B.

    1

  • C.

    \frac{a b c}{60}

  • D.

    \frac{1}{a b c}-\frac{1}{60}

  • E.

    \frac{1}{60}-\frac{1}{a b c}

Answer:A

Note that a-3 is -1 times 3-a. Likewise, b-4 is -1 times 4-b and c-5 is -1 times 5-c. Therefore, the product of the given fraction equals (-1)(-1)(-1)=(\mathbf{A})-1

Related Problems
Problem 1 2020 AMC 10 A
Problem 2 2020 AMC 10 A
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