AMC 8 Daily Practice Round 3

Complete problem set with solutions and individual problem pages

Problem 2 Medium

How many four-digit numbers are divisible by 19?

  • A.

    390

  • B.

    430

  • C.

    473

  • D.

    474

  • E.

    475

Answer:D

Let k be any positive integer so that 19k is a multiple of 19. For the smallest four-digit number, 19k>1000 and k>\frac{1000}{19}\approx 52.6. For the greatest four-digit number, 19k < 9999 and k < \frac{9999}{19}\approx 526.26. The number k can be in the range 53 to 526. Thus, there are 474 numbers in total.

Related Problems
Problem 1 AMC 8 Daily Practice Round 3
Problem 3 AMC 8 Daily Practice Round 3
Problem 4 AMC 8 Daily Practice Round 3
Problem 5 AMC 8 Daily Practice Round 3
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