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Math Expert V
Joined: 02 Sep 2009
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Positive integer y is 50 percent of 50 percent of positive  [#permalink]

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Difficulty:   15% (low)

Question Stats: 79% (01:51) correct 21% (02:08) wrong based on 1237 sessions

HideShow timer Statistics 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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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

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Math Expert V
Joined: 02 Sep 2009
Posts: 55804
Re: Positive integer y is 50 percent of 50 percent of positive  [#permalink]

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SOLUTION

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 $$x=200$$.

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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:
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 $$x=\sqr{400*100}=\sqr{400}*\sqr{100}=20*10=200$$.

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

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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
Math Expert V
Joined: 02 Sep 2009
Posts: 55804
Re: Positive integer y is 50 percent of 50 percent of positive  [#permalink]

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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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Bunuel

Ah, of course, I must be having one of those days! thanks
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GMAT 1: 760 Q50 V44 Re: Positive integer y is 50 percent of 50 percent of positive  [#permalink]

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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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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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GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: Positive integer y is 50 percent of 50 percent of positive  [#permalink]

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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.

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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 ?

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

$$y Percent * x = 100$$

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

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

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

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

$$x^2 = 40000$$

$$x = 200$$

(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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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]

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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:
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

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_________________ Re: Positive integer y is 50 percent of 50 percent of positive   [#permalink] 14 Mar 2019, 06:55
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