2013 AMC 12B Problem 3

Below is the professionally curated solution for Problem 3 of the 2013 AMC 12B, from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2013 AMC 12B solutions, or check the answer key.

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Concepts:counting integers in a range

Difficulty rating: 1100

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 $n?$

$146$

$147$

$148$

$149$

$150$

Solution:

Counting down from $201,$ the value $x$ is the $(202-x)$ th number. So $53$ is the $(202-53) = 149$ th number. Thus, the correct answer is D.

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