2006 AMC 8 Problems/Problem 24
Contents
Problem
In the multiplication problem below , , , are different digits. What is ?
Video Solution by OmegaLearn
https://youtu.be/7an5wU9Q5hk?t=3080
Video Solution
https://youtu.be/sd4XopW76ps -Happytwin
https://www.youtube.com/watch?v=Y4DXkhYthhs ~David
Solution 1
, so . Therefore, and , so .
Solution 2
Method 1: Test
Method 2: Bash it out to time
and .
, thus the answer is
Solution 3
Because , must be . Writing it out, we can see that So, must be . . Thus, our answer is . - J.L.L (Feel free to edit)
Solution 4
We know that is 1 because after you multiply the first column and you get . Noticing that the value of does not matter as long it is a digit number, let's give the value of the digit number . After doing some multiplication using the traditional method, our product is . We know that our end product has to be , so since our value of is 10 our product should be . Therefore, is 0 because is in the spot of . We are not done as the problem is asking for the value of which is just .
- LearnForEver
See Also
2006 AMC 8 (Problems • Answer Key • Resources) | ||
Preceded by Problem 23 |
Followed by Problem 25 | |
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 |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.