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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: 1. Please provide your solutions to the questions; 2. Please vote for the best solutions by pressing Kudos button; 3. Please vote for the questions themselves by pressing Kudos button; 4. Please share your views on difficulty level of the questions, so that we have most precise evaluation.

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 \(x=200\).

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: 1. Please provide your solutions to the questions; 2. Please vote for the best solutions by pressing Kudos button; 3. Please vote for the questions themselves by pressing Kudos button; 4. Please share your views on difficulty level of the questions, so that we have most precise evaluation.

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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11 Jul 2012, 01:04

I think that is at least 600, no more. If you are not really comfortable to translate into math is tricky, especially in the part of x^2. otherwise you will pick it wrong for sure
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Re: Positive integer y is 50 percent of 50 percent of positive [#permalink]

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25 Jul 2012, 10:21

looks to be lesser than 600 question. Just manipulation with what is given.
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I've failed over and over and over again in my life and that is why I succeed--Michael Jordan Kudos drives a person to better himself every single time. So Pls give it generously Wont give up till i hit a 700+

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

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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?

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?

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