AMC 8 Daily Practice Round 6

Complete problem set with solutions and individual problem pages

Problem 22 Easy

Four campers—Alice, Bob, Charlie, and Diana—play a number-reporting game around a campfire. In Round 1, Alice reports 1, Bob reports 2 and 3, Charlie reports 4, 5, 6, and Diana reports 7, 8, 9, 10. In Round 2, Alice continues with 11 through 15, maintaining the same pattern. How many numbers did Alice report in the first five rounds?

  • A.

    13

  • B.

    17

  • C.

    30

  • D.

    45

  • E.

    50

Answer:D

Alice's reporting pattern follows an arithmetic sequence where the number of terms per round increases by 4 each time: 1, 5, 9, 13, 17 terms for Rounds 1 to 5.

Using the arithmetic series sum formula:

1+5+9+13+17= \frac{(1+17)\times5}{2}=45

Final result: \boxed{45}

Related Problems
Problem 20 AMC 8 Daily Practice Round 6
Problem 21 AMC 8 Daily Practice Round 6
Problem 23 AMC 8 Daily Practice Round 6
Problem 24 AMC 8 Daily Practice Round 6
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