https://artofproblemsolving.com/wiki/api.php?action=feedcontributions&user=Nerd12345&feedformat=atomAoPS Wiki - User contributions [en]2024-03-29T08:53:34ZUser contributionsMediaWiki 1.31.1https://artofproblemsolving.com/wiki/index.php?title=2016_AMC_10B_Problems/Problem_4&diff=1447682016 AMC 10B Problems/Problem 42021-02-03T12:56:42Z<p>Nerd12345: /* Video Solution */</p>
<hr />
<div>==Problem==<br />
<br />
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?<br />
<br />
<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><br />
<br />
==Solution==<br />
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.<br />
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>.<br />
<br />
<br />
<br />
~savannahsolver<br />
UR MOM<br />
<br />
==See Also==<br />
{{AMC10 box|year=2016|ab=B|num-b=3|num-a=5}}<br />
{{MAA Notice}}</div>Nerd12345