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

2005 AMC 10B Problem 2

Attempt Problem 2 of the 2005 AMC 10B below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2005 AMC 10B solutions, or check the answer key.

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A positive number

x

has the property that

x\%

x

4.

What is

x?

2

4

10

20

40

x\%

means

\dfrac{x}{100}

Set up

\dfrac{x}{100}\cdot x=4

and solve for

x

The statement translates to

\dfrac{x}{100}\cdot x = 4,

x^2 = 400.

Since

x

is positive,

x = 20.

Thus, D is the correct answer.