2005 AMC 12B Problems/Problem 2: Difference between revisions

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.

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

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

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

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

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

Solution by franzliszt

2005 AMC 10B (Problems • Answer Key • Resources)
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 (Problems • Answer Key • Resources)
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

@@ Line 13: / Line 13: @@
 == Solution ==
+===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>":
 <math>0.01x \cdot x=4 \Rightarrow x^2 = 400 \Rightarrow x = \boxed{\text{(D)}20}.</math>
+===Solution 2===
+Use the answer choices. Upon examination, it is quite obvious that the answer is <math>\boxed{\text{(D)}20}.</math> Very fast.
+Solution by franzliszt
 == See also ==