Difference between revisions of "2001 AMC 10 Problems/Problem 7"

(Solution)
(Solution)
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If <math>x</math> is the number, then moving the decimal point four places to the right is the same as multiplying <math>x</math> by <math>10000</math>. This gives us the equation  
 
If <math>x</math> is the number, then moving the decimal point four places to the right is the same as multiplying <math>x</math> by <math>10000</math>. This gives us the equation  
<cmath>10000x=4\cdot\frac{1}{x}</cmath>.
+
<cmath>10000x=4\cdot\frac{1}{x}.</cmath>
This is equivalent to <cmath>x^2=\frac{4}{10000}</cmath>.
+
This is equivalent to <cmath>x^2=\frac{4}{10000}.</cmath>  
Since <math>x</math> is positive, it follows that <math>x=\frac{2}{100}=\boxed{(C) 0.02}</math>.
+
Since <math>x</math> is positive, it follows that <math>x=\frac{2}{100}=\boxed{(C) 0.02}.</math>
  
 
== See Also ==
 
== See Also ==

Revision as of 22:02, 27 July 2016

Problem

When the decimal point of a certain positive decimal number is moved four places to the right, the new number is four times the reciprocal of the original number. What is the original number?

$\textbf{(A) }0.0002\qquad\textbf{(B) }0.002\qquad\textbf{(C) }0.02\qquad\textbf{(D) }0.2\qquad\textbf{(E) }2$

Solution

If $x$ is the number, then moving the decimal point four places to the right is the same as multiplying $x$ by $10000$. This gives us the equation \[10000x=4\cdot\frac{1}{x}.\] This is equivalent to \[x^2=\frac{4}{10000}.\] Since $x$ is positive, it follows that $x=\frac{2}{100}=\boxed{(C) 0.02}.$

See Also

2001 AMC 10 (ProblemsAnswer KeyResources)
Preceded by
Problem 6
Followed by
Problem 8
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 AMC 10 Problems and Solutions

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