Skip to main content

2008 AMC 10B Problem 2

Problem 2 of 25EasierArithmeticProblem-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?

Answer choices

Show solution

Solution

After reversing the second row to 11,10,9,811,10,9,8 and the fourth row to 25,24,23,22,25,24,23,22, the two diagonals are 1,10,17,221,10,17,22 and 4,9,16,25.4,9,16,25. Their sums are 1+10+17+22=501+10+17+22=50 and 4+9+16+25=54,4+9+16+25=54, so the positive difference is 54−50=4.54-50=4. Thus, the correct answer is B.
AoPS wiki

Tagged: date and time · process simulation

More practice