2001 AMC 10 Problem 22

Question

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.

43

44

45

46

47

The first row, first column, and main diagonal all contain

v

So the other two entries of each match:

25+18=24+w=21+x

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.

So

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.

Problem 22 in other years