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Difference between revisions of "1990 AJHSME Problems/Problem 5"
 
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[[Category:Introductory Algebra Problems]]
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Latest revision as of 23:05, 4 July 2013

Problem

Which of the following is closest to the product $(.48017)(.48017)(.48017)$?

$\text{(A)}\ 0.011 \qquad \text{(B)}\ 0.110 \qquad \text{(C)}\ 1.10 \qquad \text{(D)}\ 11.0 \qquad \text{(E)}\ 110$

Solution 1

Clearly, \[.4<.48017<.5\] Since the function $f(x)=x^3$ is strictly increasing, we can say that \[.4^3<.48017^3<.5^3\] from which it follows that $\text{A}$ is much too small and $\text{C}$ is much too large, so $\boxed{\text{B}}$ is the answer.

Solution 2

Since $0.48017$ is quite close to $0.5$, or $\dfrac{1}{2}$, we can look for the answer choice that is just below $(\dfrac{1}{2})^3=\dfrac{1}{8}=0.125$, which would be $\boxed{\textbf{(B)}}$.

See Also

1990 AJHSME (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 AJHSME/AMC 8 Problems and Solutions

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