2008 AMC 12B Problem 2

Question

A

4 \times 4

block of calendar dates is shown. The order of the numbers in the second row is to be reversed. Then the order of the numbers in the fourth row is to be reversed. Finally, the numbers on each diagonal are to be added. What will be the positive difference between the two diagonal sums?

2

4

6

8

10

Answer: B

Concepts:arithmetic sequence pattern recognition

Difficulty rating: 1020

Small hint:

After reversing rows

2

and

4,

the rows become

1\,2\,3\,4,

11\,10\,9\,8,

15\,16\,17\,18,

25\,24\,23\,22

Big hint:

One diagonal reads

1, 10, 17, 22

and the other reads

4, 9, 16, 25

Solution:

Reversing the second and fourth rows gives the array with rows

1\,2\,3\,4,

11\,10\,9\,8,

15\,16\,17\,18,

and

25\,24\,23\,22.

The main diagonal sums to

1 + 10 + 17 + 22 = 50,

and the other diagonal sums to

4 + 9 + 16 + 25 = 54.

The positive difference is

54 - 50 = 4.

Thus, the correct answer is B.