2018 AMC 8 Problems/Problem 25
Problem 25
How many perfect cubes lie between and , inclusive?
Solution 1
We compute . We're all familiar with what is, namely , which is too small. The smallest cube greater than it is . is too large to calculate, but we notice that , which therefore clearly will be the largest cube less than . So, the required number of cubes is
Solution 2(Brute force)
First, . Then, . Now, we can see how many perfect cubes are between these two parameters. By guessing and checking because we have enough time to do this, we find that it starts from and ending with . Now, by counting how many numbers are between these, we find the answer to be
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Video Solution
https://www.youtube.com/watch?v=pbnddMinUF8 -Happytwin
See Also
2018 AMC 8 (Problems • Answer Key • Resources) | ||
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