2024 AMC 8 Problems/Problem 15
Problem
Let the letters ,,,,, represent distinct digits. Suppose is the greatest number that satisfies the equation
What is the value of ?
Solution 1
The highest that can be would have to be , and it cannot exceed that because it would exceed the -digit limit set on .
So, if we start at , we get , which would be wrong because the numbers cannot be repeated.
If we move on to and multiply by , we get , all the digits are different, so would be , which is . So, the answer is .
-Akhil Ravuri, John Adams Middle School ~ cxsmi (minor formatting edits)
Solution 2
Notice that .
Likewise, .
Therefore, we have the following equation:
.
Simplifying the equation gives
.
We can now use our equation to test each answer choice.
We have that , so we can find the sum:
.
So, the correct answer is .
- C. Ren, Thomas Grover Middle School