AMC 10 · 2008 · #2
Grade 2 arithmeticPick an answer.
The whole difficulty is keeping track of which number sits in which cell after two rows flip, so Tool #1 (Draw a Diagram) — literally rewriting the block with rows 2 and 4 reversed — removes every chance of grabbing the wrong number off a diagonal. Once the new block is drawn, Tool #7 (Identify Subproblems) splits the job into three tiny, independent calculations: sum one diagonal, sum the other, subtract.
Redraw the block after reversing
Redrawing the block makes both diagonals readable.
Draw the board exactly as it looks after the flip so you read real numbers off it, not remembered ones.
2.NBT.B.6Draw A DiagramAdd the main diagonal
One diagonal adds to 50.
Step down the diagonal one row at a time, moving one column right each row.
2.NBT.B.6Identify SubproblemsAdd the other diagonal
The other adds to 54.
This diagonal starts at the top-right corner and steps down-left, one column left each row.
2.NBT.B.6Identify SubproblemsTake the positive difference
The positive difference is 4, choice (B).
Positive difference just means subtract the smaller sum from the larger one.
The positive difference is the smaller diagonal total taken away from the larger one.
▸ Why?
Each diagonal total is the numbers along it added together, so both are ordinary sums.
▸ Why?
Comparing the two sums decides which is larger, and only that order fixes which way to subtract.
When numbers move around a grid, redraw the grid first and then read the diagonals off the new picture instead of your memory.
- Redraw the block after reversing
- Add the main diagonal
- Add the other diagonal
- Take the positive difference