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

(Created page with '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 ori…')
 
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== Problem ==
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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?
 
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?
  
 
<math> \textbf{(A) }0.0002\qquad\textbf{(B) }0.002\qquad\textbf{(C) }0.02\qquad\textbf{(D) }0.2\qquad\textbf{(E) }2 </math>
 
<math> \textbf{(A) }0.0002\qquad\textbf{(B) }0.002\qquad\textbf{(C) }0.02\qquad\textbf{(D) }0.2\qquad\textbf{(E) }2 </math>
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== Solution ==
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We can write our equation as:
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<math> \frac{x}{10000}=\frac{4}{x} </math>
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Cross-multiply and solve for x.
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<math> x^2=40000 \implies x=200 </math>.
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$ 200/10000=2/100= \boxed{\textbf{(C) }0.02}

Revision as of 15:02, 16 March 2011

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

We can write our equation as:

$\frac{x}{10000}=\frac{4}{x}$

Cross-multiply and solve for x.

$x^2=40000 \implies x=200$.

$ 200/10000=2/100= \boxed{\textbf{(C) }0.02}

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