1986 AJHSME Problems/Problem 8

Problem

In the product shown, $\text{B}$ is a digit. The value of $\text{B}$ is

\[\begin{tabular}[t]{r}
\text{B}2 \\
\times 7\text{B} \\ \hline
6396 \\
\end{tabular}\] (Error compiling LaTeX. Unknown error_msg)

$\text{(A)}\ 3 \qquad \text{(B)}\ 5 \qquad \text{(C)}\ 6 \qquad \text{(D)}\ 7 \qquad \text{(E)}\ 8$

Solution

Note that in any multiplication problem, the only 2 digits that will influence the last digit of the number will be the last digits of each number being multiplied.

So, $2 \times \text{B}$ has a units digit of $6$ , so $\text{B}$ is either $3$ or $8$ . If $\text{B}=3$ , then the product is $32\times 73$ , which is clearly too small, so $\text{B}=8$

$\boxed{\text{E}}$

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1986 AJHSME Problems/Problem 8

Problem

Solution

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