2004 AMC 10B Problems/Problem 2

Problem

How many two-digit positive integers have at least one $7$ as a digit?

$\mathrm{(A) \ } 10 \qquad \mathrm{(B) \ } 18\qquad \mathrm{(C) \ } 19 \qquad \mathrm{(D) \ } 20\qquad \mathrm{(E) \ } 30$

Solution

Ten numbers ( $70,71,\dots,79$ ) have $7$ as the tens digit. Nine numbers ( $17,27,\dots,97$ ) have it as the ones digit. Number $77$ is in both sets.

Thus the result is $10+9-1=18 \Rightarrow$ $\boxed{(B)}$ .

2004 AMC 10B (Problems • Answer Key • Resources)
Preceded by Problem 1	Followed by Problem 3
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All AMC 10 Problems and Solutions

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2004 AMC 10B Problems/Problem 2

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