Difference between revisions of "2024 AMC 10A Problems/Problem 7"
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Revision as of 17:33, 8 November 2024
Contents
[hide]Problem
The product of three integers is . What is the least possible positive sum of the three integers?
Solution 1
We notice that the optimal solution involves two negative numbers and a positive number. Thus we may split into three factors and choose negativity. We notice that , and trying other combinations does not yield lesser results so the answer is .
~eevee9406
Solution 2
We have . Let be positive, and let and be negative. Then we need . If , then is at least , so this doesn't work. If , then works, giving
~ pog, mathkiddus
See also
2024 AMC 10A (Problems • Answer Key • Resources) | ||
Preceded by Problem 6 |
Followed by Problem 8 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
All AMC 10 Problems and Solutions |
2024 AMC 12A (Problems • Answer Key • Resources) | |
Preceded by Problem 6 |
Followed by Problem 8 |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | |
All AMC 12 Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.