Difference between revisions of "2024 AMC 10A Problems/Problem 21"
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| + | {{duplicate|[[2024 AMC 10A Problems/Problem 21|2024 AMC 10A #21]] and [[2024 AMC 12A Problems/Problem 14|2024 AMC 12A #14]]}} | ||
==Problem== | ==Problem== | ||
The numbers, in order, of each row and the numbers, in order, of each column of a <math>5 \times 5</math> array of integers form an arithmetic progression of length <math>5{.}</math> The numbers in positions <math>(5, 5), \,(2,4),\,(4,3),</math> and <math>(3, 1)</math> are <math>0, 48, 16,</math> and <math>12{,}</math> respectively. What number is in position <math>(1, 2)?</math> | The numbers, in order, of each row and the numbers, in order, of each column of a <math>5 \times 5</math> array of integers form an arithmetic progression of length <math>5{.}</math> The numbers in positions <math>(5, 5), \,(2,4),\,(4,3),</math> and <math>(3, 1)</math> are <math>0, 48, 16,</math> and <math>12{,}</math> respectively. What number is in position <math>(1, 2)?</math> | ||
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==See also== | ==See also== | ||
{{AMC10 box|year=2024|ab=A|num-b=20|num-a=22}} | {{AMC10 box|year=2024|ab=A|num-b=20|num-a=22}} | ||
| + | {{AMC12 box|year=2024|ab=A|num-b=13|num-a=15}} | ||
{{MAA Notice}} | {{MAA Notice}} | ||
Revision as of 17:40, 8 November 2024
- The following problem is from both the 2024 AMC 10A #21 and 2024 AMC 12A #14, so both problems redirect to this page.
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 
![\[\begin{bmatrix} . & ? &.&.&. \\ .&.&.&48&.\\ 12&.&.&.&.\\ .&.&16&.&.\\ .&.&.&.&0\end{bmatrix}\]](http://latex.artofproblemsolving.com/2/c/a/2caa51c2881f478a1e28bf45df93c383dff268f6.png)
Solution
![\[\begin{bmatrix} 12 & 29 &46&63&80 \\ 12&24&36&48&60\\ 12&19&26&33&40\\ 12&14&16&18&20\\ 12&9&6&3&0\end{bmatrix}\]](http://latex.artofproblemsolving.com/1/3/5/13554e8c867fc72395411ed4e1b75544e34cc2f0.png)
-submitted by Astingo
See also
| 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 | |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
