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

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== Solution ==
 
== Solution ==
  
We can write our equation as:
+
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>.
<math> \frac{x}{10000}=\frac{4}{x} </math>
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This is equivalent to <cmath>x^2=\frac{4}{10000}</cmath>.  
 
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Since <math>x</math> is positive, it follows that <math>x=\frac{2}{100}=\boxed{(C) 0.02}</math>.
Cross-multiply and solve for <math> x </math>.
 
 
 
<math> x^2=40000 \implies x=200 </math>.
 
 
 
<math> 200/10000=2/100= \boxed{\textbf{(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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