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2020 AMC 12A Problem 5

Problem 5 of 25EasierAlgebraLogic

The 2525 integers from −10-10 to 14,14, inclusive, can be arranged to form a 55-by-55 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?

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Solution

The sum of the 2525 integers is (−10+14)⋅252=50.\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÷5=10.50 \div 5 = 10. Thus, C is the correct answer.
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Tagged: magic square · arithmetic sequence

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