Difference between revisions of "2013 AMC 12B Problems/Problem 3"
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| + | {{duplicate|[[2013 AMC 12B Problems|2013 AMC 12B #3]] and [[2013 AMC 10B Problems|2013 AMC 10B #4]]}} | ||
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==Problem== | ==Problem== | ||
| − | When counting from <math>3</math> to <math>201</math>, <math>53</math> is the <math>51^{st}</math> number counted. When counting backwards from <math>201</math> to <math>3</math>, <math>53</math> is the <math>n^{th}</math> number counted. What is <math>n</math>? | + | When counting from <math>3</math> to <math>201</math>, <math>53</math> is the <math>51^{\text{st}}</math> number counted. When counting backwards from <math>201</math> to <math>3</math>, <math>53</math> is the <math>n^{\text{th}}</math> number counted. What is <math>n</math>? |
<math>\textbf{(A)}\ 146 \qquad \textbf{(B)}\ 147 \qquad \textbf{(C)}\ 148 \qquad \textbf{(D)}\ 149 \qquad \textbf{(E)}\ 150</math> | <math>\textbf{(A)}\ 146 \qquad \textbf{(B)}\ 147 \qquad \textbf{(C)}\ 148 \qquad \textbf{(D)}\ 149 \qquad \textbf{(E)}\ 150</math> | ||
==Solution== | ==Solution== | ||
| − | Note that <math>n</math> is equal to the number of integers between <math>53</math> and <math>201</math>, inclusive. Thus, <math>n=201-53+1=\boxed{\textbf{(D)}149}</math> | + | Note that <math>n</math> is equal to the number of integers between <math>53</math> and <math>201</math>, inclusive. Thus, <math>n=201-53+1=\boxed{\textbf{(D)}\ 149}</math> |
== See also == | == See also == | ||
| + | {{AMC10 box|year=2013|ab=B|num-b=3|num-a=5}} | ||
{{AMC12 box|year=2013|ab=B|num-b=2|num-a=4}} | {{AMC12 box|year=2013|ab=B|num-b=2|num-a=4}} | ||
| + | {{MAA Notice}} | ||
Latest revision as of 17:47, 15 October 2024
- The following problem is from both the 2013 AMC 12B #3 and 2013 AMC 10B #4, so both problems redirect to this page.
Problem
When counting from 
to 
, 
is the 
number counted. When counting backwards from to , is the 
number counted. What is 
?
Solution
Note that is equal to the number of integers between and , inclusive. Thus, 
See also
| 2013 AMC 10B (Problems • Answer Key • Resources) | ||
| Preceded by Problem 3 |
Followed by Problem 5 | |
| 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 | ||
| 2013 AMC 12B (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 AMC 12 Problems and Solutions | |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
