2020 AMC 8

Complete problem set with solutions and individual problem pages

Problem 12 Medium

For a positive integer n, the factorial notation n! represents the product of the integers from n to 1. What value of N satisfies the following equation?

5!\cdot 9!=12\cdot N!

  • A.

    10

  • B.

    11

  • C.

    12

  • D.

    13

  • E.

    14

Answer:A

We have 5! = 2 \cdot 3 \cdot 4 \cdot 5, and 2 \cdot 5 \cdot 9! = 10 \cdot 9! = 10!. Therefore, the equation becomes 3 \cdot 4 \cdot 10! = 12 \cdot N!, and so 12 \cdot 10! = 12 \cdot N!. Cancelling the 12s, it is clear that N=\boxed{\textbf{(A) }10}.

Related Problems
Problem 10 2020 AMC 8
Problem 11 2020 AMC 8
Problem 13 2020 AMC 8
Problem 14 2020 AMC 8
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