2013 AMC 12B Problem 3

When counting from

3

201,

53

is the

51

st number counted. When counting backwards from

201

3,

53

is the

n

th number counted. What is

n?

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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.

Concepts: counting integers in a range

Problem text and solution from the LIVE past-contest archive. See also the AoPS wiki page for community solutions.