Difference between revisions of "1997 AHSME Problems/Problem 1"
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If <math>\texttt{a}</math> and <math>\texttt{b}</math> are digits for which | If <math>\texttt{a}</math> and <math>\texttt{b}</math> are digits for which | ||
| − | <math> \begin{ | + | <math> \begin{array}{ccc}& 2 & a\\ \times & b & 3\\ \hline & 6 & 9\\ 9 & 2\\ \hline 9 & 8 & 9\end{array} </math> |
then <math>\texttt{a+b =}</math> | then <math>\texttt{a+b =}</math> | ||
Latest revision as of 18:48, 10 March 2015
Problem
If 
and 
are digits for which
then 
Solution
From the units digit calculation, we see that the units digit of 
is 
. Since 
and 
is an integer, the only value of that works is is 
. As a double-check, that does work, since 
, which is the first line of the multiplication.
The second line of the multiplication can be found by doing the multiplication 
. Dividing both sides by 
gives 
.
Thus, 
, and the answer is 
.
See Also
| 1997 AHSME (Problems • Answer Key • Resources) | ||
| Preceded by First Problem |
Followed by Problem 2 | |
| 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 • 26 • 27 • 28 • 29 • 30 | ||
| All AHSME Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
