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2008 AMC 12B Problem 2

Problem 2 of 25EasierAlgebraProblem-Solving Techniques

A 4×44 \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?

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Solution

Reversing the second and fourth rows gives the array with rows 1 2 3 4,1\,2\,3\,4, 11 10 9 8,11\,10\,9\,8, 15 16 17 18,15\,16\,17\,18, and 25 24 23 22.25\,24\,23\,22. The main diagonal sums to 1+10+17+22=50,1 + 10 + 17 + 22 = 50, and the other diagonal sums to 4+9+16+25=54.4 + 9 + 16 + 25 = 54. The positive difference is 54−50=4.54 - 50 = 4. Thus, the correct answer is B.
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