Difference between revisions of "2005 AMC 12B Problems/Problem 2"

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== Solution ==
 
== Solution ==
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===Solution 1===
  
 
Since <math>x\%</math> means <math>0.01x</math>, the statement "<math>x\% \text{ of } x \text{ is 4}</math>" can be rewritten as "<math>0.01x \cdot x = 4</math>":
 
Since <math>x\%</math> means <math>0.01x</math>, the statement "<math>x\% \text{ of } x \text{ is 4}</math>" can be rewritten as "<math>0.01x \cdot x = 4</math>":
  
 
<math>0.01x \cdot x=4 \Rightarrow x^2 = 400 \Rightarrow x = \boxed{\text{(D)}20}.</math>
 
<math>0.01x \cdot x=4 \Rightarrow x^2 = 400 \Rightarrow x = \boxed{\text{(D)}20}.</math>
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===Solution 2===
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Use the answer choices. Upon examination, it is quite obvious that the answer is <math>\boxed{\text{(D)}20}.</math> Very fast.
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Solution by franzliszt
  
 
== See also ==
 
== See also ==

Revision as of 18:43, 12 July 2020

The following problem is from both the 2005 AMC 12B #2 and 2005 AMC 10B #2, so both problems redirect to this page.

Problem

A positive number $x$ has the property that $x\%$ of $x$ is $4$. What is $x$?

$\mathrm{(A)}\ 2      \qquad \mathrm{(B)}\ 4      \qquad \mathrm{(C)}\ 10      \qquad \mathrm{(D)}\ 20      \qquad \mathrm{(E)}\ 40$

Solution

Solution 1

Since $x\%$ means $0.01x$, the statement "$x\% \text{ of } x \text{ is 4}$" can be rewritten as "$0.01x \cdot x = 4$":

$0.01x \cdot x=4 \Rightarrow x^2 = 400 \Rightarrow x = \boxed{\text{(D)}20}.$

Solution 2

Use the answer choices. Upon examination, it is quite obvious that the answer is $\boxed{\text{(D)}20}.$ Very fast.


Solution by franzliszt

See also

2005 AMC 10B (ProblemsAnswer KeyResources)
Preceded by
Problem 1
Followed by
Problem 3
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
2005 AMC 12B (ProblemsAnswer KeyResources)
Preceded by
Problem 1
Followed by
Problem 3
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 12 Problems and Solutions

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