Difference between revisions of "2018 AMC 8 Problems/Problem 25"
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<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> | ||
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| + | ==Solution== | ||
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| + | We compute <math>2^8+1=257</math>. The smallest cube greater than it is <math>7^3=343</math>. <math>2^{18}+1</math> is too large to calculate, but we notice that <math>2^{18}=(2^6)^3=64^3</math> which is the largest cube less than <math>2^{18}+1</math>, Therefore the amount of cubes is <math>64-7+1= \boxed{\textbf{(E) }58}</math> | ||
{{AMC8 box|year=2018|num-b=24|after=Last Problem}} | {{AMC8 box|year=2018|num-b=24|after=Last Problem}} | ||
{{MAA Notice}} | {{MAA Notice}} | ||
Revision as of 12:35, 21 November 2018
Problem 25
How many perfect cubes lie between 
and 
, inclusive?
Solution
We compute 
. The smallest cube greater than it is 
. is too large to calculate, but we notice that 
which is the largest cube less than , Therefore the amount of cubes is 
| 2018 AMC 8 (Problems • Answer Key • Resources) | ||
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