It is currently 17 Oct 2017, 03:24

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

Positive integer y is 50 percent of 50 percent of positive

Author Message
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 41871

Kudos [?]: 128514 [0], given: 12179

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

Show Tags

02 Jul 2012, 02:05
Expert's post
9
This post was
BOOKMARKED
00:00

Difficulty:

15% (low)

Question Stats:

79% (01:26) correct 21% (01:47) wrong based on 843 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

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!
[Reveal] Spoiler: OA

_________________

Kudos [?]: 128514 [0], given: 12179

Math Expert
Joined: 02 Sep 2009
Posts: 41871

Kudos [?]: 128514 [1], given: 12179

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

Show Tags

02 Jul 2012, 02:05
1
KUDOS
Expert's post
2
This post was
BOOKMARKED
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 $$x=200$$.

_________________

Kudos [?]: 128514 [1], given: 12179

Manager
Joined: 02 Jun 2011
Posts: 150

Kudos [?]: 104 [0], given: 11

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

Show Tags

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

Kudos [?]: 104 [0], given: 11

Director
Joined: 22 Mar 2011
Posts: 610

Kudos [?]: 1057 [0], given: 43

WE: Science (Education)
Re: Positive integer y is 50 percent of 50 percent of positive [#permalink]

Show Tags

02 Jul 2012, 02:59
1
This post was
BOOKMARKED
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 $$x=\sqr{400*100}=\sqr{400}*\sqr{100}=20*10=200$$.

_________________

PhD in Applied Mathematics
Love GMAT Quant questions and running.

Kudos [?]: 1057 [0], given: 43

Senior Manager
Joined: 23 Oct 2010
Posts: 382

Kudos [?]: 392 [0], given: 73

Location: Azerbaijan
Concentration: Finance
Schools: HEC '15 (A)
GMAT 1: 690 Q47 V38
Re: Positive integer y is 50 percent of 50 percent of positive [#permalink]

Show Tags

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
_________________

Happy are those who dream dreams and are ready to pay the price to make them come true

I am still on all gmat forums. msg me if you want to ask me smth

Kudos [?]: 392 [0], given: 73

Intern
Joined: 15 Feb 2012
Posts: 33

Kudos [?]: 39 [0], given: 10

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

Show Tags

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.

Kudos [?]: 39 [0], given: 10

Manager
Joined: 02 Nov 2009
Posts: 140

Kudos [?]: 202 [0], given: 97

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

Show Tags

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

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

Kudos [?]: 202 [0], given: 97

Moderator
Joined: 01 Sep 2010
Posts: 3355

Kudos [?]: 9040 [0], given: 1152

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

Show Tags

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
_________________

Kudos [?]: 9040 [0], given: 1152

Senior Manager
Status: Prevent and prepare. Not repent and repair!!
Joined: 13 Feb 2010
Posts: 253

Kudos [?]: 124 [0], given: 282

Location: India
Concentration: Technology, General Management
GPA: 3.75
WE: Sales (Telecommunications)
Re: Positive integer y is 50 percent of 50 percent of positive [#permalink]

Show Tags

25 Jul 2012, 10:21
looks to be lesser than 600 question. Just manipulation with what is given.
_________________

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+

Kudos [?]: 124 [0], given: 282

Intern
Joined: 11 Mar 2013
Posts: 6

Kudos [?]: [0], given: 1

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

Show Tags

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

Kudos [?]: [0], given: 1

Math Expert
Joined: 02 Sep 2009
Posts: 41871

Kudos [?]: 128514 [0], given: 12179

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

Show Tags

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.
_________________

Kudos [?]: 128514 [0], given: 12179

Intern
Joined: 11 Mar 2013
Posts: 6

Kudos [?]: [0], given: 1

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

Show Tags

30 Jun 2015, 05:14
Bunuel

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

Kudos [?]: [0], given: 1

Manager
Joined: 07 Jun 2017
Posts: 95

Kudos [?]: 27 [0], given: 45

Location: India
Concentration: Technology, General Management
GMAT 1: 660 Q46 V38
GPA: 3.6
WE: Information Technology (Computer Software)
Re: Positive integer y is 50 percent of 50 percent of positive [#permalink]

Show Tags

03 Sep 2017, 22:59
y=0.25x
yx = 10000
substituting y
10000/x = 0.25 x
400 00 = x^2
then x = 200
_________________

Regards,
Naveen
email: nkmungila@gmail.com
Please press kudos if you like this post

Kudos [?]: 27 [0], given: 45

Manager
Joined: 04 May 2014
Posts: 119

Kudos [?]: 8 [0], given: 60

Location: India
WE: Sales (Mutual Funds and Brokerage)
Re: Positive integer y is 50 percent of 50 percent of positive [#permalink]

Show Tags

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

Kudos [?]: 8 [0], given: 60

Target Test Prep Representative
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 1545

Kudos [?]: 826 [0], given: 5

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

Show Tags

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

_________________

Jeffery Miller

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Kudos [?]: 826 [0], given: 5

Re: Positive integer y is 50 percent of 50 percent of positive   [#permalink] 14 Sep 2017, 10:37
Display posts from previous: Sort by