2020 AMC 10A Problem 7

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

Small hint:

The five row sums together equal the sum of all

25

integers

Big hint:

Compute the arithmetic-sequence sum from

-10

through

14

Video solution:

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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.