Difference between revisions of "2016 AMC 12B Problems/Problem 5"
(add solution) |
m (→Solution 2 (Highly not recommended): add signature) |
||
Line 30: | Line 30: | ||
* <math>6</math> days passed, reaching December <math>24</math>. | * <math>6</math> days passed, reaching December <math>24</math>. | ||
− | This gives a total of <math>2+2+3+3+2+3+2+6 \equiv 2 \pmod{7}</math> weekdays passing, which gets from Thursday to <math>\boxed{\textbf{(B)}\ \text{Saturday}}</math>. | + | This gives a total of <math>2+2+3+3+2+3+2+6 \equiv 2 \pmod{7}</math> weekdays passing, which gets from Thursday to <math>\boxed{\textbf{(B)}\ \text{Saturday}}</math>. ~[[User:emerald_block|emerald_block]] |
==See Also== | ==See Also== | ||
{{AMC12 box|year=2016|ab=B|num-b=4|num-a=6}} | {{AMC12 box|year=2016|ab=B|num-b=4|num-a=6}} | ||
{{MAA Notice}} | {{MAA Notice}} |
Revision as of 23:19, 6 November 2021
Problem
The War of started with a declaration of war on Thursday, June
,
. The peace treaty to end the war was signed
days later, on December
,
. On what day of the week was the treaty signed?
Solution
By: dragonfly
To find what day of the week it is in days, we have to divide
by
to see the remainder, and then add the remainder to the current day. We get that
has a remainder of 2, so we increase the current day by
to get
.
Note that the dates themselves (and thus leap years) can be ignored, as we only need the number of days that passed to figure out the day of the week.
Solution 2 (Highly not recommended)
is a leap year (divisible by
, but not divisible by
unless divisible by
), but June is after February so there are no leap days that need to be accounted for.
Since , the same day after
year is
weekday ahead. Since
and
, the same day after
/
days is
/
weekdays ahead.
years (
weekdays) passed, reaching June
,
.
- June
-
and July
-
(
days or
weekdays) passed, reaching July
.
- July
-
and August
-
(
days or
weekdays) passed, reaching August
.
- August-September (
weekdays) passed.
- September-October (
weekdays) passed.
- October-November (
weekdays) passed.
- November-December (
weekdays) passed, reaching December
.
days passed, reaching December
.
This gives a total of weekdays passing, which gets from Thursday to
. ~emerald_block
See Also
2016 AMC 12B (Problems • Answer Key • Resources) | |
Preceded by Problem 4 |
Followed by Problem 6 |
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 12 Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.