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 $10+9-1=\boxed{18}$ .

2004 AMC 10B (Problems • Answer Key • Resources)
Preceded by Problem 1	Followed by Problem 3
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25
All AMC 10 Problems and Solutions

Page

Toolbox

Search

2004 AMC 10B Problems/Problem 2

Problem

Solution

See also