2008 AMC 10B Problem 2

Problem 2 of 25EasierAlgebra

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?

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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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