1998 AHSME Problems/Problem 3
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 | |
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