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2016 AMC 10B Problem 4

Problem 4 of 25EasierAlgebraNumber Theory

Zoey read 1515 books, one at a time. The first book took her 11 day to read, the second book took her 22 days to read, the third book took her 33 days to read, and so on, with each book taking her 11 more day to read than the previous book. Zoey finished the first book on a Monday, and the second on a Wednesday. On what day of the week did she finish her 1515th book?

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Solution

The number of days it takes to read 1515 books is 15⋅162=120.\dfrac{ 15\cdot 16}{2} =120. Therefore, it is 120−1=119120-1=119 days after the first book is read. This is a multiple of 7,7, so the 1515th book was finished on the same day as the 11st book. Therefore, it was finished on a Monday. Thus, the correct answer is B .

More practice

Concepts: triangular number · modular arithmetic

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