Difference between revisions of "1998 AHSME Problems/Problem 3"
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If <math>\texttt{a,b,}</math> and <math>\texttt{c}</math> are digits for which | If <math>\texttt{a,b,}</math> and <math>\texttt{c}</math> are digits for which | ||
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&\ \texttt{c 7 3} \end{tabular}</math></center> | &\ \texttt{c 7 3} \end{tabular}</math></center> |
Latest revision as of 19:46, 10 March 2015
Problem 3
If and are digits for which
then
Solution
Working from right to left, we see that . Clearly if is a single digit integer, this cannot be possible. Therefore, there must be some borrowing from . Borrow from the digit , and you get , giving .
Since was borrowed from , we have from the tens column . Again for single digit integers this will not work. Again, borrow from , giving . Solving for :
Finally, since was borrowed from the hundreds column, we have , giving .
As a check, the problem is , which is a true sentence.
The desired quantity is , and the answer is .
See Also
1998 AHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 2 |
Followed by Problem 4 | |
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 |
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