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Difference between revisions of "2016 AMC 10B Problems/Problem 4"

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Zoey read <math>15</math> books, one at a time. The first book took her <math>1</math> day to read, the second book took her <math>2</math> days to read, the third book took her <math>3</math> days to read, and so on, with each book taking her <math>1</math> 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 the week did she finish her <math>15</math>th book?
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==Problem==
  
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<math>\textbf{(A)}\ Sunday\qquad\textbf{(B)}\ Monday\qquad\textbf{(C)}\ Wednesday\qquad\textbf{(D)}\ Friday\qquad\textbf{(E)}\ Saturday</math>
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Zoey read <math>15</math> books, one at a time. The first book took her <math>1</math> day to read, the second book took her <math>2</math> days to read, the third book took her <math>3</math> days to read, and so on, with each book taking her <math>1</math> 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 the week did she finish her <math>15</math>th book?
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<math>\textbf{(A)}\ \text{Sunday}\qquad\textbf{(B)}\ \text{Monday}\qquad\textbf{(C)}\ \text{Wednesday}\qquad\textbf{(D)}\ \text{Friday}\qquad\textbf{(E)}\ \text{Saturday}</math>
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==Solution==
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The process took <math>1+2+3+\ldots+13+14+15=120</math> days, so the last day was <math>119</math> days after the first day.
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Since <math>119</math> is divisible by <math>7</math>, both must have been the same day of the week, so the answer is <math>\textbf{(B)}\ \text{Monday}</math>.
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~savannahsolver
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UR MOM
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==See Also==
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{{AMC10 box|year=2016|ab=B|num-b=3|num-a=5}}
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{{MAA Notice}}

Revision as of 08:56, 3 February 2021

Problem

Zoey read $15$ books, one at a time. The first book took her $1$ day to read, the second book took her $2$ days to read, the third book took her $3$ days to read, and so on, with each book taking her $1$ 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 the week did she finish her $15$th book?

$\textbf{(A)}\ \text{Sunday}\qquad\textbf{(B)}\ \text{Monday}\qquad\textbf{(C)}\ \text{Wednesday}\qquad\textbf{(D)}\ \text{Friday}\qquad\textbf{(E)}\ \text{Saturday}$

Solution

The process took $1+2+3+\ldots+13+14+15=120$ days, so the last day was $119$ days after the first day. Since $119$ is divisible by $7$, both must have been the same day of the week, so the answer is $\textbf{(B)}\ \text{Monday}$.


~savannahsolver UR MOM

See Also

2016 AMC 10B (Problems • Answer Key • Resources)
Preceded by
Problem 3 		Followed by
Problem 5
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25
All AMC 10 Problems and Solutions

The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. AMC logo.png

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