1990 AJHSME Problems/Problem 5

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 $\boxed{\textbf{(B)}}$ .

1990 AJHSME (Problems • Answer Key • Resources)
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1990 AJHSME Problems/Problem 5

Contents

Problem

Solution 1

Solution 2

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