Difference between revisions of "2003 AMC 10B Problems/Problem 22"

(Created page with "==Problem== A clock chimes once at <math>30</math> minutes past each hour and chimes on the hour according to the hour. For example, at <math>1 \text{PM}</math> there is one chi...")
 
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Every day, there will be <math>24</math> half-hours and <math>2(1+2+3+\cdots+12)</math> chimes according to the arrow, resulting in <math>24+156=180</math> total chimes.
 
Every day, there will be <math>24</math> half-hours and <math>2(1+2+3+\cdots+12)</math> chimes according to the arrow, resulting in <math>24+156=180</math> total chimes.
  
On <math>\text{February 27},</math> the number of chimes that still need to occur is <math>2003-91=1912.</math> <math>1912/180=10\text{r}112.</math> Round up, and it is <math>11</math> days past <math>\text{February 27},</math> which is <math>\boxed{\mathrm{(B) \ } \text{March 9}}</math>
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On <math>\text{February 27},</math> the number of chimes that still need to occur is <math>2003-91=1912.</math> <math>1912/180=10\text{r}112.</math> Round up, and it is <math>11</math> days past <math>\text{February 27},</math> which is <math>\boxed{\textbf{(B) \ } \text{March 9}}</math>
  
 
==See Also==
 
==See Also==
 
{{AMC10 box|year=2003|ab=B|num-b=21|num-a=23}}
 
{{AMC10 box|year=2003|ab=B|num-b=21|num-a=23}}

Revision as of 21:00, 26 November 2011

Problem

A clock chimes once at $30$ minutes past each hour and chimes on the hour according to the hour. For example, at $1 \text{PM}$ there is one chime and at noon and midnight there are twelve chimes. Starting at $11:15 \text{AM}$ on $\text{February 26, 2003},$ on what date will the $2003\text{rd}$ chime occur?

$\textbf{(A) } \text{March 8} \qquad\textbf{(B) } \text{March 9} \qquad\textbf{(C) } \text{March 10} \qquad\textbf{(D) } \text{March 20} \qquad\textbf{(E) } \text{March 21}$

Solution

First, find how many chimes will have already happened before midnight (the beginning of the day) of $\text{February 27, 2003}.$ $13$ half-hours have passed, and the number of chimes according to the hour is $1+2+3+\cdots+12.$ The total number of chimes is $13+78=91$

Every day, there will be $24$ half-hours and $2(1+2+3+\cdots+12)$ chimes according to the arrow, resulting in $24+156=180$ total chimes.

On $\text{February 27},$ the number of chimes that still need to occur is $2003-91=1912.$ $1912/180=10\text{r}112.$ Round up, and it is $11$ days past $\text{February 27},$ which is $\boxed{\textbf{(B) \ } \text{March 9}}$

See Also

2003 AMC 10B (ProblemsAnswer KeyResources)
Preceded by
Problem 21
Followed by
Problem 23
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
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