Problem 11 · 1994 AJHSME
Hard
Logic & Word Problems
two-way-table
Last summer 100 students attended basketball camp. Of those, 52 were boys and 48 were girls. Also, 40 students were from Jonas Middle School and 60 were from Clay Middle School. Twenty of the girls were from Jonas Middle School. How many of the boys were from Clay Middle School?
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Answer: B — 32.
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Hint 1 of 2
Every student is sorted two ways at once — boy/girl AND Jonas/Clay. When two labels overlap like that, a 2×2 grid (boys/girls across, Jonas/Clay down) keeps it all straight.
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Hint 2 of 2
You're handed the Jonas girls (20). Use a row total to fill its partner, then a column total to slide over to the answer — each blank is just 'total minus the known piece.'
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Approach: fill in a two-way table
- Set up the grid. The girls' row totals 48, and 20 are from Jonas, so girls from Clay = 48 − 20 = 28.
- The Clay column totals 60. Take out the 28 Clay girls: boys from Clay = 60 − 28 = 32.
- Why the grid beats juggling sentences: every row and every column must hit its total, so each filled box instantly unlocks the next. Cross-check: Jonas boys = 52 − 32 = 20, and Jonas total 20 girls + 20 boys = 40 ✓ — the whole table balances.
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