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# Positive integer y is 50 percent of 50 percent of positive

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Positive integer y is 50 percent of 50 percent of positive [#permalink]  27 Apr 2010, 15:01
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Positive integer y is 50 percent of 50 percent of positive integer x, and y percent of x equals 100. what is the value of x ?

A) 50
B) 100
C) 200
D) 1000
E) 2000

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Last edited by zz0vlb on 27 Apr 2010, 15:29, edited 1 time in total.
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Re: 50 percent of 50 percent of positive integer [#permalink]  27 Apr 2010, 15:10
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zz0vlb wrote:
Positive integer y is 50 percent of 50 percent of positive integer x, and y percent of x equals 100. what is the value of x ?

A. 50
B. 100
C. 200
D. 1000
E. 2000

\sqrt{C - OG12}

I already solved it. Posting this for others who needs practice.

Given: $$x>0$$ and $$y>0$$.
"Positive integer y is 50 percent of 50 percent of positive integer x" --> $$y=0.5*(0.5x)=0.25x$$
"y percent of x equals 100" --> $$\frac{y}{100}*x=100$$ --> $$xy=100*100$$ --> substitute $$y$$ --> $$x^2=4*100*100$$ --> as $$x>0$$, only one solution $$x=200$$.

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Re: Positive integer y is 50 percent of 50 percent of positive [#permalink]  02 Apr 2014, 01:32
$$y = \frac{50x}{100} * \frac{50}{100}$$

$$y = \frac{25x}{100}$$ .......... (1)

$$\frac{xy}{100} = 100$$

$$y = 100 * \frac{100}{x}$$ ..... (2)

Equating (1) & (2)

$$\frac{25x}{100} = 100 * \frac{100}{x}$$

$$25 x^2 = 100 * 100 * 100$$

$$x^2 = 4 * 100 * 100$$

x = 2 * 10 * 10 = 200

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Re: Positive integer y is 50 percent of 50 percent of positive   [#permalink] 02 Apr 2014, 01:32
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