Problem 12 · 1986 AJHSME
Hard
Fractions, Decimals & Percents
diagonal-sum
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Answer: D — 40%.
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Hint 1 of 2
"Same grade on both tests" means Test-1 grade equals Test-2 grade. Where in a grid does the row label match the column label? Picture the path those cells trace.
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Hint 2 of 2
Those matching cells (A-A, B-B, C-C, D-D, F-F) run straight down the diagonal. Add just those five, then turn the count into a percent of 30.
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Approach: the matching cells form the diagonal
- A student scored the same on both tests exactly when their row (Test 1) matches their column (Test 2). In the grid those equal-label cells line up on the main diagonal — so you ignore the other 20 cells entirely.
- Add the diagonal: 2 (A-A) + 4 (B-B) + 5 (C-C) + 1 (D-D) + 0 (F-F) = 12 students.
- Convert to a fraction of the class: 12 ⁄ 30 = 0.40 = 40%.
- Why the diagonal: in any 'before vs. after' table, the diagonal is always the 'no change' group — a quick visual you can reuse for any such matrix.
Mark:
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