2021 AMC 12A Problems/Problem 3
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 by Punxsutawney Phil
https://youtube.com/watch?v=MUHja8TpKGw&t=143s
Video Solution by Hawk Math
https://www.youtube.com/watch?v=P5al76DxyHY
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 |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.