It is currently 25 Sep 2020, 02:40
My Tests

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.

x > y > w > 0

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
1 KUDOS received
Founder
Founder
User avatar
Joined: 18 Apr 2015
Posts: 13358
Followers: 288

Kudos [?]: 3392 [1] , given: 12193

CAT Tests
x > y > w > 0 [#permalink] New post 08 May 2018, 16:06
1
This post received
KUDOS
Expert's post
00:00

Question Stats:

79% (00:34) correct 20% (06:38) wrong based on 89 sessions
\(x > y > w > 0\)

Quantity A
Quantity B
\(\frac{xy}{w}\)
\(\frac{yw}{x}\)



A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.
[Reveal] Spoiler: OA

_________________

Need Practice? 20 Free GRE Quant Tests available for free with 20 Kudos
GRE Prep Club Members of the Month: Each member of the month will get three months free access of GRE Prep Club tests.

Manager
Manager
Joined: 26 Jan 2018
Posts: 189
GRE 1: Q165 V156
Followers: 1

Kudos [?]: 132 [0], given: 3

Re: x > y > w > 0 [#permalink] New post 09 May 2018, 08:45
I tried using fractions and whole numbers and in both cases its A and hence the answer.
3 KUDOS received
GRE Instructor
User avatar
Joined: 10 Apr 2015
Posts: 3834
Followers: 148

Kudos [?]: 4489 [3] , given: 69

CAT Tests
Re: x > y > w > 0 [#permalink] New post 09 May 2018, 13:02
3
This post received
KUDOS
Expert's post
Carcass wrote:
\(x > y > w > 0\)

Quantity A
Quantity B
\(\frac{xy}{w}\)
\(\frac{yw}{x}\)



A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.


We can solve this question using matching operations
Given:
Quantity A: \(\frac{xy}{w}\)

Quantity B: \(\frac{yw}{x}\)

Since we're told that w is POSITIVE, we can safely multiply both quantities by w to get:
Quantity A: \(xy\)

Quantity B: \(\frac{yw^2}{x}\)

Since we're told that x is POSITIVE, we can safely multiply both quantities by x to get:
Quantity A: \(x^2y\)
Quantity B: \(yw^2\)

Since we're told that y is POSITIVE, we can safely divide both quantities by y to get:
Quantity A: \(x^2\)
Quantity B: \(w^2\)

If x and w are both positive, AND \(x > w\), then we can be certain that \(x^2 > w^2\)

Answer: A

RELATED VIDEO FROM MY COURSE

_________________

Brent Hanneson – Creator of greenlighttestprep.com
If you enjoy my solutions, you'll like my GRE prep course.
Image
Sign up for GRE Question of the Day emails

Director
Director
Joined: 09 Nov 2018
Posts: 505
Followers: 0

Kudos [?]: 55 [0], given: 1

Re: x > y > w > 0 [#permalink] New post 20 Dec 2018, 18:34
GreenlightTestPrep wrote:

We can solve this question using matching operations
Given:
Quantity A: xy/w
Quantity B: yw/x

Since we're told that w is POSITIVE, we can safely multiply both quantities by w to get:
Quantity A: xy
Quantity B: yw²/x

Since we're told that x is POSITIVE, we can safely multiply both quantities by x to get:
Quantity A: x²y
Quantity B: yw²

Since we're told that y is POSITIVE, we can safely divide both quantities by y to get:
Quantity A: x²
Quantity B: w²

If x and w are both positive, AND x > w, then we can be certain that x² > w²

Answer: A


I am always confused with one thing... please let it clear. I did every thing right upto
Quantity A: x²
Quantity B: w²
then thought if A and B both are integer, A is bigger, but if A and B are both decimal, I mean 0<x<1 and 0<y<1, then B is bigger.
if x=1, then 0<w<1; 0<y<1 hence x>x^2, y>y^2
So ans is D. That is my confusion.
I know I am wrong in this case, do not know why? Please explain.

Last edited by AE on 21 Dec 2018, 10:19, edited 3 times in total.
Supreme Moderator
Joined: 01 Nov 2017
Posts: 371
Followers: 10

Kudos [?]: 176 [0], given: 4

Re: x > y > w > 0 [#permalink] New post 20 Dec 2018, 18:48
Expert's post
AE wrote:
GreenlightTestPrep wrote:

We can solve this question using matching operations
Given:
Quantity A: xy/w
Quantity B: yw/x

Since we're told that w is POSITIVE, we can safely multiply both quantities by w to get:
Quantity A: xy
Quantity B: yw²/x

Since we're told that x is POSITIVE, we can safely multiply both quantities by x to get:
Quantity A: x²y
Quantity B: yw²

Since we're told that y is POSITIVE, we can safely divide both quantities by y to get:
Quantity A: x²
Quantity B: w²

If x and w are both positive, AND x > w, then we can be certain that x² > w²

Answer: A


I am always confused with one thing... please let it clear. I did every thing right upto
Quantity A: x²
Quantity B: w²
then thought if A and B both are integer, A is bigger, but if A and B are both decimal then B is bigger. I know I am wrong in this, do not know why? Please explain.


If x>w>0, \(x^2>w^2\) will always be true.

May be you are getting confused with \(x^2>x\)
If 0<x<1, then \(x>x^2\)... At x=1,\(x=x^2\), but if x>1, then \(x^2>x\).
Ofcourse when x<0, \(x^2>x\)
_________________

Some useful Theory.
1. Arithmetic and Geometric progressions : https://greprepclub.com/forum/progressions-arithmetic-geometric-and-harmonic-11574.html#p27048
2. Effect of Arithmetic Operations on fraction : https://greprepclub.com/forum/effects-of-arithmetic-operations-on-fractions-11573.html?sid=d570445335a783891cd4d48a17db9825
3. Remainders : https://greprepclub.com/forum/remainders-what-you-should-know-11524.html
4. Number properties : https://greprepclub.com/forum/number-property-all-you-require-11518.html
5. Absolute Modulus and Inequalities : https://greprepclub.com/forum/absolute-modulus-a-better-understanding-11281.html

Director
Director
Joined: 09 Nov 2018
Posts: 505
Followers: 0

Kudos [?]: 55 [0], given: 1

Re: x > y > w > 0 [#permalink] New post 21 Dec 2018, 10:11
chetan2u wrote:

If x>w>0, \(x^2>w^2\) will always be true.

May be you are getting confused with \(x^2>x\)
If 0<x<1, then \(x>x^2\)... At x=1,\(x=x^2\), but if x>1, then \(x^2>x\).
Ofcourse when x<0, \(x^2>x\)


Yes That is my question
if x=1, then 0<w<1; 0<y<1 hence x>x^2, y>y^2
So ans is D. That is my confusion.
Intern
Intern
Joined: 17 Oct 2019
Posts: 5
Followers: 0

Kudos [?]: 3 [0], given: 3

Re: x > y > w > 0 [#permalink] New post 25 Apr 2020, 04:08
AE wrote:
GreenlightTestPrep wrote:

We can solve this question using matching operations
Given:
Quantity A: xy/w
Quantity B: yw/x

Since we're told that w is POSITIVE, we can safely multiply both quantities by w to get:
Quantity A: xy
Quantity B: yw²/x

Since we're told that x is POSITIVE, we can safely multiply both quantities by x to get:
Quantity A: x²y
Quantity B: yw²

Since we're told that y is POSITIVE, we can safely divide both quantities by y to get:
Quantity A: x²
Quantity B: w²

If x and w are both positive, AND x > w, then we can be certain that x² > w²

Answer: A


I am always confused with one thing... please let it clear. I did every thing right upto
Quantity A: x²
Quantity B: w²
then thought if A and B both are integer, A is bigger, but if A and B are both decimal, I mean 0<x<1 and 0<y<1, then B is bigger.
if x=1, then 0<w<1; 0<y<1 hence x>x^2, y>y^2
So ans is D. That is my confusion.
I know I am wrong in this case, do not know why? Please explain.




I actually have the same question. Can anyone please explain? I think there is no restriction so the variables can be positive fractions. In this case the answer is D. I am confused.
1 KUDOS received
GRE Instructor
User avatar
Joined: 10 Apr 2015
Posts: 3834
Followers: 148

Kudos [?]: 4489 [1] , given: 69

CAT Tests
Re: x > y > w > 0 [#permalink] New post 25 Apr 2020, 05:13
1
This post received
KUDOS
Expert's post
Narek wrote:
AE wrote:
I am always confused with one thing... please let it clear. I did every thing right upto
Quantity A: x²
Quantity B: w²
then thought if A and B both are integer, A is bigger, but if A and B are both decimal, I mean 0<x<1 and 0<y<1, then B is bigger.
if x=1, then 0<w<1; 0<y<1 hence x>x^2, y>y^2
So ans is D. That is my confusion.
I know I am wrong in this case, do not know why? Please explain.



I actually have the same question. Can anyone please explain? I think there is no restriction so the variables can be positive fractions. In this case the answer is D. I am confused.


I think you may be conflating a few different properties:

Property #1: If 0 < x < y, then x² < y²
Property #2: If x < y < 0, then x² > y²



Property #3: If 0 < x < 1, then x² < x
Property #4: If 1 < x, then x < x²


Notice that properties #1 and #2, compare the SQUARES of two DIFFERENT variables (x² and y²), whereas properties #3 and #4, compare DIFFERENT POWERS of the SAME variable (x and x²)

Does that help?
_________________

Brent Hanneson – Creator of greenlighttestprep.com
If you enjoy my solutions, you'll like my GRE prep course.
Image
Sign up for GRE Question of the Day emails

Re: x > y > w > 0   [#permalink] 25 Apr 2020, 05:13
Display posts from previous: Sort by

x > y > w > 0

  Question banks Downloads My Bookmarks Reviews Important topics  


GRE Prep Club Forum Home| About| Terms and Conditions and Privacy Policy| GRE Prep Club Rules| Contact

Powered by phpBB © phpBB Group

Kindly note that the GRE® test is a registered trademark of the Educational Testing Service®, and this site has neither been reviewed nor endorsed by ETS®.