2024 AMC 10A Problems/Problem 21
- The following problem is from both the 2024 AMC 10A #21 and 2024 AMC 12A #14, so both problems redirect to this page.
Contents
[hide]Problem
The numbers, in order, of each row and the numbers, in order, of each column of a array of integers form an arithmetic progression of length The numbers in positions and are and respectively. What number is in position
Solution
-submitted by Astingo
Solution 2: Some Basic Algebra and Answer Choices
Assume the number in position is . The integer in position will be , as and average out to x. Similarly, the integer in position is . The integer in position is . This makes the number in position .
The only answer choice that makes x an integer is
~ElaineGu
(Note: I'm not very good at writing solutions or latex, so people who wish to edit this solution to be more understandable may do so.)
Solution 3 (Arithmetic Sequences)
Start from the . Going up, let the common difference be , and going left, let the common difference be . Therefore, we have ~Tacos_are_yummy_1 (I'm currently editing this, please don't interfere, thanks!)
See also
This problem is remarkably similar to 1988 AIME Problems/Problem 6.
2024 AMC 10A (Problems • Answer Key • Resources) | ||
Preceded by Problem 20 |
Followed by Problem 22 | |
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 10 Problems and Solutions |
2024 AMC 12A (Problems • Answer Key • Resources) | |
Preceded by Problem 13 |
Followed by Problem 15 |
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 |
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