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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] New post 27 Apr 2010, 15:01
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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

GMAT Official Guide 12

Question: 12
Page: 22
Difficulty: 700

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Video Explanations:
[Reveal] Spoiler: OA

Last edited by zz0vlb on 27 Apr 2010, 15:29, edited 1 time in total.
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Re: 50 percent of 50 percent of positive integer [#permalink] New post 27 Apr 2010, 15:10
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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 \(x=200\).

Answer: C.
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Re: Positive integer y is 50 percent of 50 percent of positive [#permalink] New post 02 Apr 2014, 01:32
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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

Answer = C
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Re: Positive integer y is 50 percent of 50 percent of positive [#permalink] New post 09 Dec 2015, 12:02
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Re: Positive integer y is 50 percent of 50 percent of positive [#permalink] New post 10 Dec 2015, 05:54
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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] New post 23 Dec 2015, 05:53
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

GMAT Official Guide 12

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] New post 26 Dec 2015, 08:41
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.

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:
[Reveal] Spoiler:
C


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Re: Positive integer y is 50 percent of 50 percent of positive   [#permalink] 26 Dec 2015, 08:41
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