2020 AMC 10A Problem 7

Problem 7 of 25EasierAlgebra

The

25

integers from

-10

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?

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Solution

The sum of the integers from

-10

14

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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