AMC 10 Daily Practice Round 1

Complete problem set with solutions and individual problem pages

Problem 18 Medium

If k is a positive integer such that the product 935 \times 972 \times 975 \times k has its last four digits as zeros, what is sum of the digits of the minimum value of k?

  • A.

    2

  • B.

    6

  • C.

    10

  • D.

    15

  • E.

    18

Answer:A

935 = 5 \times 11 \times 17,

972 = 2^2 \times 3^5,

975 = 3 \times 5^2 \times 13.

To ensure that the last four digits are zeros, at least two more factors of 2 and one more factor of 5 are needed.

Thus, the minimum value of k is: 2^2 \times 5 = 20.

Therefore, the answer is 20.

Related Problems
Problem 16 AMC 10 Daily Practice Round 1
Problem 17 AMC 10 Daily Practice Round 1
Problem 19 AMC 10 Daily Practice Round 1
Problem 20 AMC 10 Daily Practice Round 1
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