2001 AMC 10 Problem 22

Problem 22 of 25HarderAlgebra Logic

In the magic square shown, the sums of the numbers in each row, column, and diagonal are the same. Five of these numbers are represented by

v,

w,

x,

y,

and

z.

Find

y+z.

Show solution

Solution

Since

v

sits in the first row, first column, and main diagonal, the remaining two entries of each of those lines have equal sums:

25+18=24+w=21+x.

w=19

and

x=22.

The anti-diagonal

25,

22,

19

sums to

66,

so the magic sum is

66.

Then

v=66-24-19=23,

y=66-18-22=26,

and

z=66-25-21=20.

Hence

y+z=46.

Thus, the correct answer is D.

Tagged: magic square · linear equation