1986 AHSME Problems/Problem 4

Problem

Let S be the statement "If the sum of the digits of the whole number $n$ is divisible by $6$ , then $n$ is divisible by $6$ ."

A value of $n$ which shows $S$ to be false is

$\textbf{(A)}\ 30 \qquad \textbf{(B)}\ 33 \qquad \textbf{(C)}\ 40 \qquad \textbf{(D)}\ 42 \qquad \textbf{(E)}\ \text{ none of these}$

Solution

For a counterexample, we need a number whose digit sum is divisible by $6$ , but which is not itself divisible by $6$ . $33$ satisfies these conditions, as $3+3=6$ but $6$ does not divide $33$ , so the answer is $\boxed{B}$ .

1986 AHSME (Problems • Answer Key • Resources)
Preceded by Problem 3	Followed by Problem 5
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1986 AHSME Problems/Problem 4

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