2005 AMC 12B Problems/Problem 2

Revision as of 21:24, 26 November 2013 by Mathcool2009 (talk | contribs) (Solution)
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

Since $x \text{%}$ (Error compiling LaTeX. Unknown error_msg) means $0.01x$, the statement "$x \text{ % of } x \text{ is 4}$ (Error compiling LaTeX. Unknown error_msg)" can be rewritten as "$0.01x \cdot x = 4$":

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

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