During AMC testing, the AoPS Wiki is in read-only mode. No edits can be made.

Difference between revisions of "1988 AJHSME Problems/Problem 6"

m
(Solution 2)
 
(4 intermediate revisions by 2 users not shown)
Line 7: Line 7:
 
==Solution==
 
==Solution==
 
Converting the [[decimal|decimals]] to [[fraction|fractions]] gives us <math>\frac{(.2)^3}{(.02)^2} =\frac{\left( \frac{1}{5}\right)^3}{\left(\frac{1}{50}\right)^2}=\frac{50^2}{5^3}=\frac{2500}{125}=20\Rightarrow \mathrm{(E)}</math>.
 
Converting the [[decimal|decimals]] to [[fraction|fractions]] gives us <math>\frac{(.2)^3}{(.02)^2} =\frac{\left( \frac{1}{5}\right)^3}{\left(\frac{1}{50}\right)^2}=\frac{50^2}{5^3}=\frac{2500}{125}=20\Rightarrow \mathrm{(E)}</math>.
 +
 +
==Solution 2==
 +
 +
We expand <math>\frac{(0.2)^3}{(0.02)^2}</math>, and get <math>\frac{(0.2) \times (0.2) \times (0.2)}{(0.02) \times (0.02)}</math>. The two <math>0.02</math>'s "cancel" out with the two <math>0.2</math>'s, leaving the fraction as: <math>(10) \times (10) \times (0.2)</math>. Using basic calculations, we compute this expression to get <math>20\Rightarrow \mathrm{(E)}</math>.
 +
 +
~sakshamsethi
  
 
==See Also==
 
==See Also==
Line 12: Line 18:
 
{{AJHSME box|year=1988|num-b=5|num-a=7}}
 
{{AJHSME box|year=1988|num-b=5|num-a=7}}
 
[[Category:Introductory Algebra Problems]]
 
[[Category:Introductory Algebra Problems]]
 +
{{MAA Notice}}

Latest revision as of 11:04, 28 July 2020

Problem

$\frac{(.2)^3}{(.02)^2} =$

$\text{(A)}\ .2 \qquad \text{(B)}\ 2 \qquad \text{(C)}\ 10 \qquad \text{(D)}\ 15 \qquad \text{(E)}\ 20$

Solution

Converting the decimals to fractions gives us $\frac{(.2)^3}{(.02)^2} =\frac{\left( \frac{1}{5}\right)^3}{\left(\frac{1}{50}\right)^2}=\frac{50^2}{5^3}=\frac{2500}{125}=20\Rightarrow \mathrm{(E)}$.

Solution 2

We expand $\frac{(0.2)^3}{(0.02)^2}$, and get $\frac{(0.2) \times (0.2) \times (0.2)}{(0.02) \times (0.02)}$. The two $0.02$'s "cancel" out with the two $0.2$'s, leaving the fraction as: $(10) \times (10) \times (0.2)$. Using basic calculations, we compute this expression to get $20\Rightarrow \mathrm{(E)}$.

~sakshamsethi

See Also

1988 AJHSME (ProblemsAnswer KeyResources)
Preceded by
Problem 5
Followed by
Problem 7
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

The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. AMC logo.png

Invalid username
Login to AoPS