2016 AMC 10A Problems/Problem 5
Contents
[hide]Problem
A rectangular box has integer side lengths in the ratio . Which of the following could be the volume of the box?
Solution 1
Let the smallest side length be . Then the volume is . If , then
Solution 2
As seen in the first solution, we end up with . Taking the answer choices and dividing by , we get , , , , and the final answer has to equal . The only answer choice that works is .
Solution 3 (quick)
Clearly, the volume is a multiple of . Since itself is not an option, the next possibility is .
~Technodoggo
Video Solution (HOW TO THINK CREATIVELY!!!)
https://youtu.be/bc-somFWrbg
~Education, the Study of Everything
Video Solution
https://youtu.be/VIt6LnkV4_w?t=512
~savannahsolver
https://www.youtube.com/watch?v=4zTfNAWEzys
~IBHishere
See Also
2016 AMC 10A (Problems • Answer Key • Resources) | ||
Preceded by Problem 4 |
Followed by Problem 6 | |
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 |
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