Difference between revisions of "2014 CEMC Gauss (Grade 8) Problems/Problem 11"
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John was born on a Wednesday. Alison was born 72 days later. On what day of the week was Alison born? | John was born on a Wednesday. Alison was born 72 days later. On what day of the week was Alison born? | ||
| − | <math> \text{ (A) }\ Thursday \qquad\text{ (B) }\ Monday \qquad\text{ (C) }\ Sunday \qquad\text{ (D) }\ Saturday \qquad\text{ (E) }\ Friday </math> | + | <math> \text{ (A) }\ \text{Thursday} \qquad\text{ (B) }\ \text{Monday} \qquad\text{ (C) }\ \text{Sunday} \qquad\text{ (D) }\ \text{Saturday} \qquad\text{ (E) }\ \text{Friday} </math> |
==Solution== | ==Solution== | ||
A week has <math>7</math> days, so the days of the week repeat every <math>7</math> days. <math>7</math> goes into <math>72</math> ten times, but with a remainder of <math>2</math>. Thus, we need to know what day of the week is <math>2</math> days after Wednesday. | A week has <math>7</math> days, so the days of the week repeat every <math>7</math> days. <math>7</math> goes into <math>72</math> ten times, but with a remainder of <math>2</math>. Thus, we need to know what day of the week is <math>2</math> days after Wednesday. | ||
| − | The day of the week that is <math>2</math> days after Wednesday is <math>\boxed {\textbf {(E) } Friday}</math>. | + | The day of the week that is <math>2</math> days after Wednesday is <math>\boxed {\textbf {(E) } \text{Friday}}</math>. |
~anabel.disher | ~anabel.disher | ||
| + | {{CEMC box|year=2014|competition=Gauss (Grade 8)|num-b=10|num-a=12}} | ||
Latest revision as of 11:34, 18 October 2025
Problem
John was born on a Wednesday. Alison was born 72 days later. On what day of the week was Alison born?
Solution
A week has 
days, so the days of the week repeat every days. goes into 
ten times, but with a remainder of 
. Thus, we need to know what day of the week is days after Wednesday.
The day of the week that is days after Wednesday is 
.
~anabel.disher
| 2014 CEMC Gauss (Grade 8) (Problems • Answer Key • Resources) | ||
| Preceded by Problem 10 |
Followed by Problem 12 | |
| 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 | ||
| CEMC Gauss (Grade 8) | ||
