2008 AMC 10B Problem 2

Below is the professionally curated solution for Problem 2 of the 2008 AMC 10B, from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2008 AMC 10B solutions, or check the answer key.

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Concepts:date and time process simulation

Difficulty rating: 880

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:

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.

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