2013 AMC 12B Problems/Problem 3

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 $3$ to $201$ , $53$ is the $51^{st}$ number counted. When counting backwards from $201$ to $3$ , $53$ is the $n^{th}$ number counted. What is $n$ ?

$\textbf{(A)}\ 146 \qquad \textbf{(B)}\ 147 \qquad \textbf{(C)}\ 148 \qquad \textbf{(D)}\ 149 \qquad \textbf{(E)}\ 150$

Solution

Note that $n$ is equal to the number of integers between $53$ and $201$ , inclusive. Thus, $n=201-53+1=\boxed{\textbf{(D)}\ 149}$

2013 AMC 12B (Problems • Answer Key • Resources)
Preceded by Problem 2	Followed by Problem 4
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2013 AMC 12B Problems/Problem 3

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