Problem 4 · 1992 AJHSME
Medium
Fractions, Decimals & Percents
percent
During the softball season, Judy had 35 hits. Among her hits were 1 home run, 1 triple, and 5 doubles. The rest of her hits were singles. What percent of her hits were singles?
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Answer: E — 80%.
Show hints
Hint 1 of 3
The listed hits (home run, triple, doubles) are the FEW; singles are everything else. Is it easier to count the few and subtract, or count the many directly?
Still stuck? Show hint 2 →
Hint 2 of 3
When most of a group is one thing, count the small leftover pile and subtract from the total — the complement is the shortcut.
Still stuck? Show hint 3 →
Hint 3 of 3
Once you have the number of singles, "what percent" just means singles ÷ total.
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Approach: count the small pile (non-singles), subtract, then take the percent
- Only a few hits are named, so count those: 1 home run + 1 triple + 5 doubles = 7 non-singles. Everything else is a single: 35 − 7 = 28 singles.
- Percent of singles = 28 ÷ 35. Since 28/35 = 4/5, that's 80%.
- Why this transfers: when one category dominates, it's faster to count its complement (the leftovers) and subtract than to tally the big group directly — the same move shows up in probability ("at least one" problems) all the time.
- Sanity check: 7 non-singles is one-fifth of 35, so singles must be the other four-fifths — 80% — matching our answer.
Mark:
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