2013 AMC 10B Problem 4

Below is the professionally curated solution for Problem 4 of the 2013 AMC 10B, from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2013 AMC 10B solutions, or check the answer key.

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Concepts:counting integers in a range

Difficulty rating: 720

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:

When counting backward, $201$ is the first number, $200$ is the second, and in general $x$ is the $202-x$ th number.

Thus $53$ is the $202-53=149$ th number counted.

Thus, the correct answer is D .

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