1997 AJHSME Problems/Problem 5
Problem
There are many two-digit multiples of 7, but only two of the multiples have a digit sum of 10. The sum of these two multiples of 7 is
Solution 1 (brute force)
Writing out all two digit numbers that have a digital sum of , you get and . The two numbers on that list that are divisible by are and . Their sum is , choice .
Solution 2
Writing out all the two digit multiples of , you get and . Again you find and have a digital sum of , giving answer .
You may notice that adding either increases the digital sum by , or decreases it by , depending on whether there is carrying or not.
See also
1997 AJHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 4 |
Followed by Problem 6 | |
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