Problem 21 · 1992 AJHSME
Hard
Fractions, Decimals & Percents
read-graphpercent-comparison
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Answer: B — February.
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Hint 1 of 3
It says greatest PERCENT, not greatest amount. The same 2-unit lead is a huge deal over a tiny bar but barely noticeable over a tall one. So where should you look?
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Hint 2 of 3
Percent difference compares the gap to the SMALLER bar, not to the chart. The same gap looks biggest where the bars are shortest — hunt for the lowest pair.
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Hint 3 of 3
Find the month where one bar is a large fraction of the other, e.g. one bar is double the other.
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Approach: the same gap is a bigger PERCENT over short bars — check the smallest month
- Percent difference measures how big the gap is relative to the smaller bar. So scan for the month with the shortest bars, where even a small lead is a large share.
- February is by far the lowest: drums show 4 and bugles show 2. Drums exceed bugles by 2, and 2 is 100% of the bugles' 2 — the drums are double.
- No other month comes close: e.g. April (drums 5, bugles 7) is only a 40% gap, March is a tie. So the greatest percent difference is in February.
- Why this transfers: ‘greatest percent’ almost never means ‘tallest bars’ — it means ‘biggest ratio,’ which favors small numbers. A lead of 2 is trivial next to 50 but enormous next to 2. Always compare the gap to the smaller value.
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