Difference between revisions of "1986 AJHSME Problems/Problem 8"

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==See Also==
 
==See Also==
  
[[1986 AJHSME Problems]]
+
{{AJHSME box|year=1986|num-b=7|num-a=9}}
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[[Category:Introductory Number Theory Problems]]
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[[Category:Introductory Algebra Problems]]

Revision as of 18:55, 20 May 2009

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. ! Missing $ inserted.)

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

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 $\text{B}=8$

$\boxed{\text{E}}$

See Also

1986 AJHSME (ProblemsAnswer KeyResources)
Preceded by
Problem 7
Followed by
Problem 9
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 AJHSME/AMC 8 Problems and Solutions
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