AMC 10 Weekly Practice Round 3

Complete problem set with solutions and individual problem pages

Problem 16 Medium

If one number is chosen at random from all the positive divisors of 2025, what is the probability that this number is a perfect square?

  • A.

    0.4

  • B.

    0.3

  • C.

    0.6

  • D.

    0.7

  • E.

    0.8

Answer:A

Since 2025 = 3^{4} \times 5^{2},

 

the positive divisors of 2025 are

1, 3, 5, 9, 15, 25, 27, 45, 75, 81, 135, 225, 405, 675, 2025,

a total of 15 numbers.

 

Among them, the perfect squares are

1, 9, 25, 81, 225, 2025,

a total of 6 numbers.

 

Therefore, if one number is chosen at random from all the positive divisors of 2025, the probability that it is a perfect square is

\dfrac{6}{15} = \dfrac{2}{5}.

 

Hence, the answer is \dfrac{2}{5}.

Related Problems
Problem 14 AMC 10 Weekly Practice Round 3
Problem 15 AMC 10 Weekly Practice Round 3
Problem 17 AMC 10 Weekly Practice Round 3
Problem 18 AMC 10 Weekly Practice Round 3
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