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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 ProjectPositive 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 ProjectEach 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!
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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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Bunuel wrote: The Official Guide for GMAT® Review, 13th Edition  Quantitative Questions ProjectPositive 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 ProjectEach 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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Positive integer y is 50 percent of 50 percent of positive integ [#permalink]
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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 Answer = C
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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?
Thanks



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Re: Positive integer y is 50 percent of 50 percent of positive [#permalink]
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30 Jun 2015, 03:50



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Re: Positive integer y is 50 percent of 50 percent of positive [#permalink]
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30 Jun 2015, 05:14
BunuelAh, 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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10 Dec 2015, 06:54
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 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
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. Let's TEST Answer B: 100 IF.... X = 100 Y = (.5)(.5)(100) = 25 25% of 100 = 25 (but it's supposed to be 100). This answer is TOO SMALL. Let's TEST Answer D: 1000 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. Final Answer: GMAT assassins aren't born, they're made, Rich
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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) Hence, Answer is C
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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
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 Answer: C
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Re: Positive integer y is 50 percent of 50 percent of positive [#permalink]
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09 Mar 2018, 11:01
Bunuel wrote: The Official Guide for GMAT® Review, 13th Edition  Quantitative Questions ProjectPositive 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 ProjectEach 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! Hello everyone happy to see you all i think this problem can be solved logically if if y is 50 percent of 50 percent of positive integer x which implies that X is twice bigger number than y and if y percent of x equals 100  this means that 50 percent of 50 percent of positive integer x = 100 ( hence y = 100 and x = 200) y = .50 (200) = 100 it means that answer must be 200 options D and E are eliminated stright away because x can not be bigger number. likewise A and B are out cant be equal or smaller than 50% of x YAY




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