Difference between revisions of "2008 AMC 8 Problems/Problem 3"
(Created page with "==Problem 3== If February is a month that contains Friday the <math>13^{\text{th}}</math>, what day of the week is February 1? <math>\textbf{(A)}\ \text{Sunday} \qquad \textbf{(...") |
Prezlink16 (talk | contribs) (→Solution 3) |
||
| (8 intermediate revisions by 5 users not shown) | |||
| Line 1: | Line 1: | ||
| − | ==Problem | + | ==Problem== |
If February is a month that contains Friday the <math>13^{\text{th}}</math>, what day of the week is February 1? | If February is a month that contains Friday the <math>13^{\text{th}}</math>, what day of the week is February 1? | ||
| Line 7: | Line 7: | ||
\textbf{(D)}\ \text{Thursday}\qquad | \textbf{(D)}\ \text{Thursday}\qquad | ||
\textbf{(E)}\ \text{Saturday} </math> | \textbf{(E)}\ \text{Saturday} </math> | ||
| + | |||
| + | ==Solution== | ||
| + | We can go backwards by days, but we can also backwards by weeks. If we go backwards by weeks, we see that February 6 is a Friday. If we now go backwards by days, February 1 is a <math>\boxed{\textbf{(A)}\ \text{Sunday}}</math> | ||
| + | |||
| + | ==Solution 2== | ||
| + | Since the days of the week repeat every 7 days and <math>1-13\equiv2\pmod7</math>, the day of the week of the day 2 days after February 13 is the same as the day of the week of February 1. Since we know that February 13 is a Friday, the day of the week of the day 2 days after February 13 is a Sunday so we get that February 1 is a <math>\boxed{\textbf{(A)}\ \text{Sunday}}</math>. | ||
| + | |||
| + | ==Solution 3== | ||
| + | We can go back 2 weeks and say that Friday is the -1st of February. Going forward 2 days, we get that February 1st is Sunday. So our answer is <math>\boxed{\textbf{(A)}\ \text{Sunday}}</math>. | ||
==See Also== | ==See Also== | ||
{{AMC8 box|year=2008|num-b=2|num-a=4}} | {{AMC8 box|year=2008|num-b=2|num-a=4}} | ||
| + | {{MAA Notice}} | ||
Latest revision as of 10:21, 24 August 2023
Problem
If February is a month that contains Friday the 
, what day of the week is February 1?
Solution
We can go backwards by days, but we can also backwards by weeks. If we go backwards by weeks, we see that February 6 is a Friday. If we now go backwards by days, February 1 is a 
Solution 2
Since the days of the week repeat every 7 days and 
, the day of the week of the day 2 days after February 13 is the same as the day of the week of February 1. Since we know that February 13 is a Friday, the day of the week of the day 2 days after February 13 is a Sunday so we get that February 1 is a .
Solution 3
We can go back 2 weeks and say that Friday is the -1st of February. Going forward 2 days, we get that February 1st is Sunday. So our answer is .
See Also
| 2008 AMC 8 (Problems • Answer Key • Resources) | ||
| Preceded by Problem 2 |
Followed by Problem 4 | |
| 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 AJHSME/AMC 8 Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
