Problem 6 · 1989 AJHSME
Medium
Arithmetic & Operations
number-linespacing
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Answer: C — 12.
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Hint 1 of 3
What's the same about every gap between neighboring ticks? Use the part you DO know — the stretch from 0 to 20 — to measure one gap.
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Hint 2 of 3
On an evenly-spaced line, find one gap's value first, then a point's value is just (number of gaps from 0) × (gap value).
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Hint 3 of 3
Count the gaps, not the tick marks: between 0 and 20 there are 5 gaps, and y sits 3 gaps to the right of 0.
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Approach: measure one gap, then count gaps to y
- The known stretch from 0 to 20 is split into 5 equal gaps, so each gap is worth 20 ÷ 5 = 4. This is the key move: use the labeled span to calibrate a single step.
- Now count gaps from 0 to y: there are 3 of them, so y = 3 × 4 = 12.
- Trap to avoid: count the spaces between ticks, never the ticks themselves. Six tick marks make only 5 gaps — off-by-one here would give a wrong step size and a wrong y.
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