2020 AMC 10 B

Complete problem set with solutions and individual problem pages

Problem 7 Easy

How many positive even multiples of 3 less than 2020 are perfect squares? (2020 AMC 10B, Question #7)

  • A.

    7

  • B.

    8

  • C.

    9

  • D.

    10

  • E.

    12

Answer:A

Any even multiple of 3 is a multiple of 6 , so we need to find multiples of 6 that are perfect squares and less than 2020 . Any solution that we want will be in the form (6 n)^{2}, where n is a positive integer. The smallest possible value is at n=1, and the largest is at n=7 (where the expression equals 1764 ). Therefore, there are a total of (A) 7 possible numbers.