Question

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?

$2$

$5$

$10$

$25$

$50$

Answer: C

Concepts:magic square arithmetic sequence

Difficulty rating: 960

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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.

2020 AMC 10A Problem 7

Answer: C

Difficulty rating: 960

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Written solution:

Problem 7 in Other Years