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

(Solution 1)
(Solution 2)
 
(2 intermediate revisions by the same user not shown)
Line 22: Line 22:
 
===Solution 2===
 
===Solution 2===
  
Use the answer choices. Upon examination, it is quite obvious that the answer is <math>\boxed{\text{(D)}20}.</math> Very fast.
+
Try the answer choices one by one. Upon examination, it is quite obvious that the answer is <math>\boxed{\textbf{(D) }20}.</math> Very fast.
  
  

Latest revision as of 13:56, 14 December 2021

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 $x$?

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

Solution

Solution 1

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

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

Solution 2

Try the answer choices one by one. Upon examination, it is quite obvious that the answer is $\boxed{\textbf{(D) }20}.$ 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

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