Problem 25 · 2022 Math Kangaroo
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Logic & Word Problems
sum-constraintcasework
Twelve weights have integer masses of 1 g, 2 g, 3 g, …, 11 g and 12 g respectively. A vendor divides those weights up into 3 groups of 4 weights each. The total mass of the first group is 41 g, the mass of the second group is 26 g (see diagram). Which of the following weights is in the same group as the weight with 9 g?
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Answer: C — 7 g
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Hint 1 of 2
The three groups sum to 1+2+...+12 = 78; you know two group totals.
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Hint 2 of 2
Find the third group's total, then see which 4-weight set containing 9 g fits a group total.
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Approach: use group sums to place the 9 g weight
- All weights sum to 78; with groups of 41 and 26, the third group totals 78 - 41 - 26 = 11.
- The 9 g weight is too heavy for the 11 g group, so it lies in the 41 g or 26 g group.
- Working out which four weights total 41 and which total 26, the weight grouped with 9 g among the options is 7 g.
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