Difference between revisions of "2021 AMC 12A Problems/Problem 3"
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| + | ==Video Solution== | ||
| + | https://youtu.be/d2musztzDjw | ||
| + | -pi_is_3.14 | ||
==See also== | ==See also== | ||
{{AMC12 box|year=2021|ab=A|num-b=2|num-a=4}} | {{AMC12 box|year=2021|ab=A|num-b=2|num-a=4}} | ||
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Revision as of 15:00, 11 February 2021
Contents
Problem
The sum of two natural numbers is 
. One of the two numbers is divisible by 
. If the units digit of that number is erased, the other number is obtained. What is the difference of these two numbers?
Solution
The units digit of a multiple of will always be 
. We add a whenever we multiply by . So, removing the units digit is equal to dividing by .
Let the smaller number (the one we get after removing the units digit) be 
. This means the bigger number would be 
.
We know the sum is 
so 
. So 
. The difference is 
. So, the answer is 
.
--abhinavg0627
Video Solution
https://youtu.be/d2musztzDjw -pi_is_3.14
See also
| 2021 AMC 12A (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 | |
| All AMC 12 Problems and Solutions | |
These problems are copyrighted © by the Mathematical Association of America, as part of the American Mathematics Competitions. 
