Difference between revisions of "2013 AMC 10A Problems/Problem 13"
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Summing, we get <math>40 + 8 + 6 + 4 + 2 = \boxed{\textbf{(B) }60}</math> | Summing, we get <math>40 + 8 + 6 + 4 + 2 = \boxed{\textbf{(B) }60}</math> | ||
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+ | ==Video Solution== | ||
+ | https://youtu.be/YXBC8gCVnNE | ||
+ | |||
+ | ~savannahsolver | ||
==See Also== | ==See Also== |
Revision as of 21:03, 17 December 2020
Contents
Problem
How many three-digit numbers are not divisible by , have digits that sum to less than , and have the first digit equal to the third digit?
Solution
We use a casework approach to solve the problem. These three digit numbers are of the form .( denotes the number ). We see that and , as does not yield a three-digit integer and yields a number divisible by 5.
The second condition is that the sum . When is , , , or , can be any digit from to , as . This yields numbers.
When , we see that so . This yields more numbers.
When , so . This yields more numbers.
When , so . This yields more numbers.
When , so . This yields more numbers.
Summing, we get
Video Solution
~savannahsolver
See Also
2013 AMC 10A (Problems • Answer Key • Resources) | ||
Preceded by Problem 12 |
Followed by Problem 14 | |
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 | ||
All AMC 10 Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.