Difference between revisions of "2010 AMC 8 Problems/Problem 22"
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Latest revision as of 08:06, 10 March 2023
Contents
Problem
The hundreds digit of a three-digit number is 
more than the units digit. The digits of the three-digit number are reversed, and the result is subtracted from the original three-digit number. What is the units digit of the result?
Solution 1
Let the hundreds, tens, and units digits of the original three-digit number be 
, 
, and 
, respectively. We are given that 
. The original three-digit number is equal to 
. The hundreds, tens, and units digits of the reversed three-digit number are , , and , respectively. This number is equal to 
. Subtracting this expression from the expression for the original number, we get 
. Thus, the units digit in the final result is 
Solution 2
The result must hold for any three-digit number with hundreds digit being more than the units digit. 
is such a number. Evaluating, we get 
. Thus, the units digit in the final result is
Solution 3
Set the units digit of the original number as 
. Thus, its hundreds digit is 
. After the digits are reversed, the hundreds digit of the original number will be the units digit of the new number. Since 
, we can do regrouping and "borrow" 
from the tens digit and bring it to the units digit as a 
. Therefore, the units digit will end up as 
Video by MathTalks
Video Solution by WhyMath
~savannahsolver
See Also
| 2010 AMC 8 (Problems • Answer Key • Resources) | ||
| Preceded by Problem 21 |
Followed by Problem 23 | |
| 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 AJHSME/AMC 8 Problems and Solutions | ||
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