GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 20 Oct 2018, 21:07

Close

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
Your Progress

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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

Positive integer y is 50 percent of 50 percent of positive

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 50007
Positive integer y is 50 percent of 50 percent of positive  [#permalink]

Show Tags

New post 02 Jul 2012, 02:05
3
11
00:00
A
B
C
D
E

Difficulty:

  15% (low)

Question Stats:

80% (01:51) correct 20% (02:10) wrong based on 1207 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:
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!

_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 50007
Re: Positive integer y is 50 percent of 50 percent of positive  [#permalink]

Show Tags

New post 02 Jul 2012, 02:05
1
1
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 \(x=200\).

Answer: C.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Director
Director
User avatar
Joined: 22 Mar 2011
Posts: 601
WE: Science (Education)
Re: Positive integer y is 50 percent of 50 percent of positive  [#permalink]

Show Tags

New post 02 Jul 2012, 02:59
1
1
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:
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
_________________

PhD in Applied Mathematics
Love GMAT Quant questions and running.

SVP
SVP
User avatar
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1829
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
Positive integer y is 50 percent of 50 percent of positive integ  [#permalink]

Show Tags

New post 02 Apr 2014, 02:32
4
\(y = \frac{50x}{100} * \frac{50}{100}\)

\(y = \frac{25x}{100}\) .......... (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
_________________

Kindly press "+1 Kudos" to appreciate :)

Intern
Intern
avatar
Joined: 11 Mar 2013
Posts: 6
Re: Positive integer y is 50 percent of 50 percent of positive  [#permalink]

Show Tags

New post 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
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 50007
Re: Positive integer y is 50 percent of 50 percent of positive  [#permalink]

Show Tags

New post 30 Jun 2015, 03:50
1
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.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Intern
Intern
avatar
Joined: 11 Mar 2013
Posts: 6
Re: Positive integer y is 50 percent of 50 percent of positive  [#permalink]

Show Tags

New post 30 Jun 2015, 05:14
Bunuel

Ah, of course, I must be having one of those days! thanks
Senior Manager
Senior Manager
User avatar
Joined: 20 Aug 2015
Posts: 391
Location: India
GMAT 1: 760 Q50 V44
Re: Positive integer y is 50 percent of 50 percent of positive  [#permalink]

Show Tags

New post 10 Dec 2015, 06:54
1
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
Intern
Intern
avatar
Joined: 23 Dec 2015
Posts: 8
Re: Positive integer y is 50 percent of 50 percent of positive  [#permalink]

Show Tags

New post 23 Dec 2015, 06:53
1
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
EMPOWERgmat Instructor
User avatar
V
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 12687
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: Positive integer y is 50 percent of 50 percent of positive  [#permalink]

Show Tags

New post 26 Dec 2015, 09:41
1
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
_________________

760+: Learn What GMAT Assassins Do to Score at the Highest Levels
Contact Rich at: Rich.C@empowergmat.com

Rich Cohen

Co-Founder & GMAT Assassin

Special Offer: Save $75 + GMAT Club Tests Free
  Official GMAT Exam Packs + 70 Pt. Improvement Guarantee
www.empowergmat.com/

*****Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!*****

Retired Moderator
User avatar
P
Joined: 19 Mar 2014
Posts: 948
Location: India
Concentration: Finance, Entrepreneurship
GPA: 3.5
GMAT ToolKit User Premium Member
Re: Positive integer y is 50 percent of 50 percent of positive  [#permalink]

Show Tags

New post 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
_________________

"Nothing in this world can take the place of persistence. Talent will not: nothing is more common than unsuccessful men with talent. Genius will not; unrewarded genius is almost a proverb. Education will not: the world is full of educated derelicts. Persistence and determination alone are omnipotent."

Best AWA Template: https://gmatclub.com/forum/how-to-get-6-0-awa-my-guide-64327.html#p470475

Target Test Prep Representative
User avatar
P
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 3896
Location: United States (CA)
Re: Positive integer y is 50 percent of 50 percent of positive  [#permalink]

Show Tags

New post 28 Jun 2017, 17:02
1
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
_________________

Scott Woodbury-Stewart
Founder and CEO

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

Director
Director
User avatar
P
Joined: 09 Mar 2016
Posts: 942
Re: Positive integer y is 50 percent of 50 percent of positive  [#permalink]

Show Tags

New post 09 Mar 2018, 11:01
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:
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 :)
GMAT Club Bot
Re: Positive integer y is 50 percent of 50 percent of positive &nbs [#permalink] 09 Mar 2018, 11:01
Display posts from previous: Sort by

Positive integer y is 50 percent of 50 percent of positive

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


Copyright

GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.