AMC 8 Daily Practice Round 8

Complete problem set with solutions and individual problem pages

Problem 22 Easy

Amy is reading a novel. She read 1 page on the first day, 2 pages on the second day, 3 pages on the third day, etc, until the total of pages she has read is a multiple of 90. How many pages does she read in total by then?

  • A.

    580

  • B.

    600

  • C.

    630

  • D.

    650

  • E.

    680

Answer:C

Let Amy have read 90m pages up to day n.

From the problem statement:

1 + 2 + 3 + \cdots + n = 90m

\frac{(n+1)n}{2} = 90m

(n+1)n = 180m

n(n+1) = 2^{2} \times 3^{2} \times 5 \times m

n(n+1) = 36 \times 5m

Therefore, when m = 7, n = 35.

90 \times 7 = 630

Answer: Amy read a total of 630 pages, \text{C}.

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