Difference between revisions of "1986 AJHSME Problems/Problem 8"
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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. | 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, <math>2 \times B | + | So, <math>2 \times \text{B}</math> has a units digit of <math>6</math>, so <math>\text{B}</math> is either <math>3</math> or <math>8</math>. If <math>\text{B}=3</math>, then the product is <math>32\times 73</math>, which is clearly too small, so <math>\text{B}=8</math> |
| + | |||
| + | <math>\boxed{\text{E}}</math> | ||
==See Also== | ==See Also== | ||
[[1986 AJHSME Problems]] | [[1986 AJHSME Problems]] | ||
Revision as of 11:33, 24 January 2009
Problem
In the product shown, 
is a digit. The value of is
\[\begin{tabular}[t]{r}
\text{B}2 \\
\times 7\text{B} \\ \hline
6396 \\
\end{tabular}\] (Error compiling LaTeX. Unknown error_msg)
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, 
has a units digit of 
, so is either 
or 
. If 
, then the product is 
, which is clearly too small, so 
