AMC12 2005 B

AMC12 2005 B · Q2

AMC12 2005 B · Q2. It mainly tests Quadratic equations, Percent.

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

一个正数 $x$ 具有这样的性质：$x$ 的 $x\%$ 是 $4$。$x$ 是多少？

(A) 2 2

(B) 4 4

(D) 20 20

(E) 40 40

Answer

Correct choice: (D)

正确答案：（D）

Solution

Since $x\%$ means $0.01x$, the statement "$x\% \text{ of } x \text{ is 4}$" can be rewritten as "$0.01x \cdot x = 4$": $0.01x \cdot x=4 \Rightarrow x^2 = 400 \Rightarrow x = \boxed{\textbf{(D) }20}.$ 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

由于 $x\%$ 表示 $0.01x$，陈述“$x\% \text{ of } x \text{ is 4}$”可以改写为“$0.01x \cdot x = 4$”： $0.01x \cdot x=4 \Rightarrow x^2 = 400 \Rightarrow x = \boxed{\textbf{(D) }20}.$ 逐一代入选项检验。经过检查，很明显答案是 $\boxed{\textbf{(D) }20}.$ 非常快。 Solution by franzliszt

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