2020 AMC 12A Problem 5

Below is the professionally curated solution for Problem 5 of the 2020 AMC 12A, from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2020 AMC 12A solutions, or check the answer key.

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Concepts:magic square arithmetic sequence

Difficulty rating: 1130

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?

$2$

$5$

$10$

$25$

$50$

Solution:

The sum of the $25$ integers is $\dfrac{(-10 + 14) \cdot 25}{2} = 50.$

The five rows each have the same sum and together account for the total, so each row sums to $50 \div 5 = 10.$

Thus, C is the correct answer.

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