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2004 AMC 10B Problems/Problem 2

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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=\boxed{18}.

See also

2004 AMC 10B (ProblemsResources)
Preceded by
Problem 1
Followed by
Problem 3
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