2023 AMC 8 Problems/Problem 4

Problem

The numbers from 1 to 49 are arranged in a spiral pattern on a square grid, beginning at the center. The first few numbers have been entered into the grid below. Consider the four numbers that will appear in the shaded squares, on the same diagonal as the number 7. How many of these four numbers are prime?

$\textbf{(A)}\ 0 \qquad \textbf{(B)}\ 1 \qquad \textbf{(C)}\ 2 \qquad \textbf{(D)}\ 3 \qquad \textbf{(E)}\ 4$

Solution 1

First, we fill out the entire grid. We find that the $4$ numbers are $39,19,23,47$ . The numbers $19,23,$ and $47$ are prime, so there are $\boxed{\textbf{(D) }3}$ prime numbers.

~MathFun1000 (minor edits apex304)

Solution 2

Fill out the entire grid to count that there are $\boxed{\text{(D)}3}$ prime numbers -apex304

Video Solution by Magic Square

https://youtu.be/-N46BeEKaCQ?t=5392

2023 AMC 8 (Problems • Answer Key • Resources)
Preceded by Problem 3	Followed by Problem 5
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All AJHSME/AMC 8 Problems and Solutions

The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.

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2023 AMC 8 Problems/Problem 4

Contents

Problem

Solution 1

Solution 2

Video Solution by Magic Square

See Also