Difference between revisions of "2018 AMC 8 Problems/Problem 25"
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==Problem 25== | ==Problem 25== | ||
| − | How many perfect cubes lie between <math>2^8+1</math> and <math>2^{18}+1</math>, inclusive ? | + | How many perfect cubes lie between <math>2^8+1</math> and <math>2^{18}+1</math>, inclusive? |
<math>\textbf{(A) }4\qquad\textbf{(B) }9\qquad\textbf{(C) }10\qquad\textbf{(D) }57\qquad \textbf{(E) }58</math> | <math>\textbf{(A) }4\qquad\textbf{(B) }9\qquad\textbf{(C) }10\qquad\textbf{(D) }57\qquad \textbf{(E) }58</math> | ||
Revision as of 02:14, 2 December 2018
Problem 25
How many perfect cubes lie between 
and 
, inclusive?
Solution
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 . Therefore, the required number of cubes is 
See Also
| 2018 AMC 8 (Problems • Answer Key • Resources) | ||
| Preceded by Problem 24 |
Followed by Last Problem | |
| 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 AJHSME/AMC 8 Problems and Solutions | ||
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