2020 AMC 10A Problem 7

Below is the video solution and professionally curated solution for Problem 7 of the 2020 AMC 10A, from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2020 AMC 10A solutions, or check the answer key.

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Concepts:magic square arithmetic sequence

Difficulty rating: 960

The $25$ integers from $-10$ to $14,$ inclusive, can be arranged to form a $5$ -by- $5$ square in which the sum of the numbers in each row, the sum of the numbers in each column, and the sum of the numbers along each of the main diagonals are all the same. What is the value of this common sum?

$2$

$5$

$10$

$25$

$50$

Video solution:

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Written solution:

The sum of the integers from $-10$ to $14$ is $25\cdot\dfrac{-10+14}{2}=50$ . If every row has common sum $S$ , then the five row sums add to $50$ , so $5S=50$ and $S=10$ . Thus, C is the correct answer.

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