🇺🇸 AMC 8 ⇄ switch contest
1986 AJHSME

Problem 16

Problem 16 · 1986 AJHSME Hard
Fractions, Decimals & Percents percent-of-total
Figure for AJHSME 1986 Problem 16
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Answer: A — 2.5.
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Hint 1 of 3
The winter bar is hidden, so you can't read it — but the other three bars *are* readable, and the 25% fact secretly tells you the grand total. What is 25% as a simple fraction, and what does that say about the total?
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Hint 2 of 3
25% means 'one quarter,' so Fall is a quarter of the whole year — making the total four times the Fall bar. Find the total, then subtract the three visible bars to uncover winter.
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Hint 3 of 3
Read the bars: Spring 4.5, Summer 5, Fall 4. The total is 4 × Fall.
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Approach: use 25% to recover the total, then subtract the visible seasons
  1. The covered bar can't be measured, so come at it from the total instead. 25% is exactly one quarter, and Fall is that quarter, so the whole year = 4 × Fall = 4 × 4 = 16 million.
  2. Read the three uncovered bars: Spring 4.5, Summer 5, Fall 4 (total 13.5 million).
  3. Winter is whatever's left of the total: 16 − 13.5 = 2.5 million.
  4. Why this works: a hidden value in a 'parts add to a whole' setup is best found as total − (everything else) — and a tidy percent like 25% is your shortcut to that total.
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