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: 1130

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.

2020 AMC 12A Problem 5

Answer: C

Difficulty rating: 1130

Solution:

Problem 5 in Other Years