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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]

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27 Apr 2010, 16:01
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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

Official Guide 12 Question

 Question: 12 Page: 22 Difficulty: 700

Find All Official Guide Questions

Video Explanations:
[Reveal] Spoiler: OA

Last edited by zz0vlb on 27 Apr 2010, 16:29, edited 1 time in total.

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Re: 50 percent of 50 percent of positive integer [#permalink]

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27 Apr 2010, 16:10
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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]

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02 Apr 2014, 02:32
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$$y = \frac{50x}{100} * \frac{50}{100}$$

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

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09 Dec 2015, 13:02
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Re: Positive integer y is 50 percent of 50 percent of positive [#permalink]

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10 Dec 2015, 06:54
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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

Given:
x >0 and y > 0
y = $$\frac{50}{100}$$($$\frac{50}{100}$$*x) = 0.25x - (i)
$$\frac{y}{100}$$*x = 100. Hence xy = 10000 - (ii)

Required: Value of x
Substituting the value of y in (ii)

x*0.25x = 10000
$$x^2$$ = 100*100*100/25 = 4*100*100
x = 200 and - 200
We will consider only the positive value as we are told that x > 0

x = 200
Option C
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Re: Positive integer y is 50 percent of 50 percent of positive [#permalink]

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23 Dec 2015, 06:53
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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

Official Guide 12 Question

 Question: 12 Page: 22 Difficulty: 700

Find All Official Guide Questions

Video Explanations:

y = 50% of 50% of x = (1/2)*(1/2)*x = x/4

(y/100)x=100
x^2/400 = 100
x = 200

IMO - C

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Re: Positive integer y is 50 percent of 50 percent of positive [#permalink]

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26 Dec 2015, 09:41
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Expert's post
Hi All,

This question can be solved by TESTing THE ANSWERS.

We're told that:
1) Positive integer Y is 50 percent of 50 percent of positive integer X
2) Y percent of X equals 100

We're asked for the value of X.

IF....
X = 100
Y = (.5)(.5)(100) = 25
25% of 100 = 25 (but it's supposed to be 100). This answer is TOO SMALL.

IF....
X = 1000
Y = (.5)(.5)(1000) = 250
250% of 1000 = 2500 (but it's supposed to be 100). This answer is TOO BIG.

The likely correct answer is C, but we can TEST it rather easily...

IF....
X = 200
Y = (.5)(.5)(200) = 50
50% of 200 = 100. This is an exact MATCH for what we were told, so this MUST be the answer.

[Reveal] Spoiler:
C

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Re: Positive integer y is 50 percent of 50 percent of positive [#permalink]

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24 Jun 2017, 16:42
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Re: Positive integer y is 50 percent of 50 percent of positive [#permalink]

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26 Jun 2017, 06:54
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 ?

$$y = \frac{50}{100} * \frac{50}{100} * x$$

$$y Percent * x = 100$$

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

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

$$x = \frac{(100 * 100)}{(50/100) * (50/100) * x}$$

$$x^2 =\frac{(100 * 100 * 100 * 100)}{(50 * 50)}$$

$$x^2 = 40000$$

$$x = 200$$

(We are not taking other value of -200 as it is given that x is positive number)

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Re: Positive integer y is 50 percent of 50 percent of positive [#permalink]

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28 Jun 2017, 17:02
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Expert's post
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

We can create the following equations:

y = (0.5)(0.5)x

y = 0.25x

and

(y/100)x = 100

Substitute y = 0.25x into the above equation:

(0.25x/100)x = 100

0.25x^2 = 10,000

x^2 = 40,000

x = 200

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Re: Positive integer y is 50 percent of 50 percent of positive   [#permalink] 28 Jun 2017, 17:02
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