2018 AMC 12B Problems/Problem 15

Problem

How many odd positive 3-digit integers are divisible by 3 but do not contain the digit 3?

$\textbf{(A) } 96 \qquad \textbf{(B) } 97 \qquad \textbf{(C) } 98 \qquad \textbf{(D) } 102 \qquad \textbf{(E) } 120$

Solution

There are $4$ choices for the last digit ( $1, 5, 7, 9$ ), and $8$ choices for the first digit (exclude $0$ ). We know what the second digit mod $3$ is, so there are $3$ choices for it (pick from one of the sets $\{0, 6, 9\},\{1, 4, 7\}, \{2, 5, 8\}$ ). The answer is $4\cdot 8 \cdot 3 = \boxed{96}$ (Plasma_Vortex)

2018 AMC 12B (Problems • Answer Key • Resources)
Preceded by Problem 14	Followed by Problem 16
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All AMC 12 Problems and Solutions

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2018 AMC 12B Problems/Problem 15

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