Difference between revisions of "1990 AJHSME Problems/Problem 5"
5849206328x (talk | contribs) (Created page with '==Problem== Which of the following is closest to the product <math>(.48017)(.48017)(.48017)</math>? <math>\text{(A)}\ 0.011 \qquad \text{(B)}\ 0.110 \qquad \text{(C)}\ 1.10 \qq…') |
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<math>\text{(A)}\ 0.011 \qquad \text{(B)}\ 0.110 \qquad \text{(C)}\ 1.10 \qquad \text{(D)}\ 11.0 \qquad \text{(E)}\ 110</math> | <math>\text{(A)}\ 0.011 \qquad \text{(B)}\ 0.110 \qquad \text{(C)}\ 1.10 \qquad \text{(D)}\ 11.0 \qquad \text{(E)}\ 110</math> | ||
| − | ==Solution== | + | ==Solution 1== |
Clearly, <cmath>.4<.48017<.5</cmath> | Clearly, <cmath>.4<.48017<.5</cmath> | ||
Since the function <math>f(x)=x^3</math> is strictly increasing, we can say that <cmath>.4^3<.48017^3<.5^3</cmath> | Since the function <math>f(x)=x^3</math> is strictly increasing, we can say that <cmath>.4^3<.48017^3<.5^3</cmath> | ||
from which it follows that <math>\text{A}</math> is much too small and <math>\text{C}</math> is much too large, so <math>\boxed{\text{B}}</math> is the answer. | from which it follows that <math>\text{A}</math> is much too small and <math>\text{C}</math> is much too large, so <math>\boxed{\text{B}}</math> is the answer. | ||
| − | + | ==Solution 2== | |
| + | Since <math>0.48017</math> is quite close to <math>0.5</math>, or <math>\dfrac{1}{2}</math>, we can look for the answer choice that is just below <math>(\dfrac{1}{2})^3=\dfrac{1}{8}=0.125</math>, which would be <math>\boxed{\textbf{(B)}}</math>. | ||
==See Also== | ==See Also== | ||
{{AJHSME box|year=1990|num-b=4|num-a=6}} | {{AJHSME box|year=1990|num-b=4|num-a=6}} | ||
[[Category:Introductory Algebra Problems]] | [[Category:Introductory Algebra Problems]] | ||
Revision as of 14:24, 28 August 2011
Contents
Problem
Which of the following is closest to the product 
?
Solution 1
Clearly, ![\[.4<.48017<.5\]](http://latex.artofproblemsolving.com/7/6/e/76e1fb23c88c587901dafb7af1ba320f63ffa66d.png)
Since the function 
is strictly increasing, we can say that ![\[.4^3<.48017^3<.5^3\]](http://latex.artofproblemsolving.com/3/3/3/333524b7a80bb9d7d2a89fa8dbfd6932913cb4d0.png)
from which it follows that 
is much too small and 
is much too large, so 
is the answer.
Solution 2
Since 
is quite close to 
, or 
, we can look for the answer choice that is just below 
, which would be 
.
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 | ||
