2008 AMC 12B Problem 2

Below is the professionally curated solution for Problem 2 of the 2008 AMC 12B, from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2008 AMC 12B solutions, or check the answer key.

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Concepts:arithmetic sequence pattern recognition

Difficulty rating: 1020

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?

$2$

$4$

$6$

$8$

$10$

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.

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