2008 AMC 10B 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:date and time process simulation

Difficulty rating: 880

Small hint:

After reversing rows

2

and

4,

write out the new grid

Big hint:

The main diagonal reads

1,10,17,22

and the other reads

4,9,16,25

Solution:

After reversing the second row to

11,10,9,8

and the fourth row to

25,24,23,22,

the two diagonals are

1,10,17,22

and

4,9,16,25.

Their sums are

1+10+17+22=50

and

4+9+16+25=54,

so the positive difference is

54-50=4.

Thus, the correct answer is B.