2024 AMC 10B Problems/Problem 24
Problem
Let How many of the values , , , and are integers?
Solution (The simplest way)
Here is the English translation with selective LaTeX formatting:
First, we know that and must be integers since they are both divisible by .
Then Let’s consider the remaining two numbers. Since they are not divisible by , the result of the first term must be a certain number , and the result of the second term must be a certain number . Similarly, the remaining two terms must each be . Their sum is , so and are also integers.
Therefore, the answer is .
See also
2024 AMC 10B (Problems • Answer Key • Resources) | ||
Preceded by Problem 23 |
Followed by Problem 25 | |
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