Difference between revisions of "2024 AMC 10A Problems/Problem 21"
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| + | ==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> | ||
| + | <cmath> \begin{bmatrix} . & ? &.&.&. \\ .&.&.&48&.\\ 12&.&.&.&.\\ .&.&16&.&.\\ .&.&.&.&0\end{bmatrix}</cmath> | ||
| + | <math>\textbf{(A) } 19 \qquad \textbf{(B) } 24 \qquad \textbf{(C) } 29 \qquad \textbf{(D) } 34 \qquad \textbf{(E) } 39</math> | ||
| + | ==Solution== | ||
Revision as of 16:52, 8 November 2024
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)
