2017 AMC 8 Problems/Problem 11

Problem 11

A square-shaped floor is covered with congruent square tiles. If the total number of tiles that lie on the two diagonals is 37, how many tiles cover the floor? what does diagonals mean

$\textbf{(A) }148\qquad\textbf{(B) }324\qquad\textbf{(C) }361\qquad\textbf{(D) }1296\qquad\textbf{(E) }1369$

Solution

Since the number of tiles lying on both diagonals is $37$ , counting one tile twice, there are $37=2x-1\implies x=19$ tiles on each side. Hence, our answer is $19^2=361=\boxed{\textbf{(C)}\ 361}$ .

2017 AMC 8 (Problems • Answer Key • Resources)
Preceded by Problem 10	Followed by Problem 12
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All AJHSME/AMC 8 Problems and Solutions

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2017 AMC 8 Problems/Problem 11

Problem 11

Solution

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