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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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The Official Guide for GMAT® Review, 13th Edition - Quantitative Questions Project

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) 1,000
(E) 2,000

Diagnostic Test
Question: 12
Page: 22
Difficulty: 650


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

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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) 1,000
(E) 2,000

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 \(x=200\).

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

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New post 02 Jul 2012, 02:58
y = 50% of 50% 0f x
= x/4
and

y/100 of x = 100

y /100 *4y =100
y = 50
and x= 200

Answer - C

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

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Bunuel wrote:
The Official Guide for GMAT® Review, 13th Edition - Quantitative Questions Project

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) 1,000
(E) 2,000

Diagnostic Test
Question: 12
Page: 22
Difficulty: 650


GMAT Club is introducing a new project: The Official Guide for GMAT® Review, 13th Edition - Quantitative Questions Project

Each week we'll be posting several questions from The Official Guide for GMAT® Review, 13th Edition and then after couple of days we'll provide Official Answer (OA) to them along with a slution.

We'll be glad if you participate in development of this project:
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2. Please vote for the best solutions by pressing Kudos button;
3. Please vote for the questions themselves by pressing Kudos button;
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Thank you!


The first information can be rewritten as \(y=0.5*0.5x=0.25x=\frac{x}{4}\), while the second information can be translated into \(\frac{y}{100}x=100\).
If we substitute y from the first equation into the second one, we get \(\frac{x}{400}x=100\), from which \(x^2=400*100\), or \(x=\sqr{400*100}=\sqr{400}*\sqr{100}=20*10=200\).

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

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New post 03 Jul 2012, 10:05
y=(1/2)*(1/2)*x =>x=4y
(y/100)*x=100 => y^2=100*100/4 y=100/2=50

x=4*50=200
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Re: Positive integer y is 50 percent of 50 percent of positive [#permalink]

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New post 03 Jul 2012, 11:43
Given that Y= (50%)*(50%)*X
Y=(50/100)*(50/100)*X
Y=(1/2)*(1/2)*X ---------------{1}


and also,

(Y%)*(X) = 100
(Y/100)*X = 100
Y=(100*100)/X

from {1}

(1/2)*(1/2)*X = (100 *100)/X
X^2 = 2*2*100*100

so, X=200.

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

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New post 09 Jul 2012, 19:36
I think this is a 300-500 level problem

are you sure it is a 650 level .. doubt it

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

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

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New post 25 Jul 2012, 10:21
looks to be lesser than 600 question. Just manipulation with what is given.
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Re: Positive integer y is 50 percent of 50 percent of positive [#permalink]

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New post 30 Jun 2015, 03:45
I need help understanding a pretty basic bit of substitution in the first explanation (I'm tired!). How do you jump from xy = 100 x 100 to x^2 = 4 x 100 x 100?

Thanks

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

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New post 30 Jun 2015, 03:50
jackrim1 wrote:
I need help understanding a pretty basic bit of substitution in the first explanation (I'm tired!). How do you jump from xy = 100 x 100 to x^2 = 4 x 100 x 100?

Thanks



\(xy=100*100\) and \(y=0.25x=\frac{x}{4}\);

\(x*\frac{x}{4}=100*100\);

\(x^2=4*100*100\).

Hope it's clear.
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Re: Positive integer y is 50 percent of 50 percent of positive [#permalink]

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New post 30 Jun 2015, 05:14
Bunuel

Ah, of course, I must be having one of those days! thanks

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

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New post 03 Sep 2017, 22:59
y=0.25x
yx = 10000
substituting y
10000/x = 0.25 x
400 00 = x^2
then x = 200
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Re: Positive integer y is 50 percent of 50 percent of positive [#permalink]

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New post 11 Sep 2017, 04:42
Easy way. Use answer choice and start from the middle.
Let x=200
50% of X=100
50% of 100=50
y=50
Now y(50%) of x(200)=100

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

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New post 14 Sep 2017, 10:37
Bunuel 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) 1,000
(E) 2,000


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

Answer: C
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Re: Positive integer y is 50 percent of 50 percent of positive   [#permalink] 14 Sep 2017, 10:37
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