1986 AJHSME Problems/Problem 8

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Problem

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

$\begin{tabular}[t]{r}\text{B}2 \\\times 7\text{B} \\ \hline6396 \\\end{tabular}$

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

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 $\text{B}=8$

$\boxed{\text{E}}$

1986 AJHSME (Problems • Resources)
Preceded by Problem 7	Followed by Problem 9
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1986 AJHSME Problems/Problem 8

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