It is currently 23 Sep 2020, 08:16
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.

x2 > y2 and x > –|y|

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
Retired Moderator
User avatar
Joined: 07 Jun 2014
Posts: 4803
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 171

Kudos [?]: 2915 [0], given: 394

x2 > y2 and x > –|y| [#permalink] New post 02 Sep 2018, 07:32
Expert's post
00:00

Question Stats:

58% (00:51) correct 41% (00:34) wrong based on 58 sessions
\(x^2 > y^2\) and \(x > -|y|\)

Quantity A
Quantity B
x
y


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

_________________

Sandy
If you found this post useful, please let me know by pressing the Kudos Button

Try our free Online GRE Test

2 KUDOS received
Active Member
Active Member
Joined: 29 May 2018
Posts: 126
Followers: 0

Kudos [?]: 110 [2] , given: 4

Re: x2 > y2 and x > –|y| [#permalink] New post 03 Sep 2018, 10:26
2
This post received
KUDOS
sandy wrote:
\(x^2 > y^2\) and \(x > -|y|\)

Quantity A
Quantity B
x
y


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.


Given \(x^2 > y^2\) and \(x > -|y|\)

From \(x^2 > y^2\) => \(x^2\) - \(y^2\) > 0 => ( x + y ) ( x - y ) > 0.

Here ( x + y ) ( x - y ) > 0 either both should be +ve or both -ve to be greater than 0.

But from \(x > -|y|\) we get ( x + y ) > 0 ( Note here |y| is converted to y )

Since we came to know that ( x + y ) > 0 then must be ( x - y ) > 0

So ( x - y ) > 0 => x > y.

A.
2 KUDOS received
Intern
Intern
Joined: 28 Aug 2018
Posts: 28
GRE 1: Q170 V166
WE: Other (Education)
Followers: 1

Kudos [?]: 30 [2] , given: 0

Re: x2 > y2 and x > –|y| [#permalink] New post 03 Sep 2018, 15:40
2
This post received
KUDOS
if \(x^2>y^2\), then \(|x|>|y|\)

if x>0 y>0, then x>y since \(|x|>|y|\);

if x>0 y<0, then x>y. Because \(x>-|y|\) and \(-|y|=-(-y)=y\);

x<0 y>0 is not possible. Because \(x>-|y|\) and \(-|y|=-y\), so \(x>-y\), which means \(|x|<|y|\), but we already know \(|x|>|y|\), so this is a contradiction;

x<0 y<0 is also not possbile, Because \(x>-|y|\) and \(-|y|=-(-y)=y\) therefore x>y but then \(|x|<|y|\), and we already know \(|x|>|y|\), so this is a contradiction;
_________________

Yuan Liu, Creator of Gregory. Dartmouth Grad.

For More GRE Math Resources

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

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

Re: x2 > y2 and x > –|y| [#permalink] New post 02 Jan 2019, 11:21
Yuan wrote:
if \(x^2>y^2\), then \(|x|>|y|\)

if x>0 y>0, then x>y since \(|x|>|y|\);

if x>0 y<0, then x>y. Because \(x>-|y|\) and \(-|y|=-(-y)=y\);

x<0 y>0 is not possible. Because \(x>-|y|\) and \(-|y|=-y\), so \(x>-y\), which means \(|x|<|y|\), but we already know \(|x|>|y|\), so this is a contradiction;

x<0 y<0 is also not possbile, Because \(x>-|y|\) and \(-|y|=-(-y)=y\) therefore x>y but then \(|x|<|y|\), and we already know \(|x|>|y|\), so this is a contradiction;


\(x>-y\), which means \(|x|<|y|\)
How please explain?
Supreme Moderator
Joined: 01 Nov 2017
Posts: 371
Followers: 10

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

Re: x2 > y2 and x > –|y| [#permalink] New post 02 Jan 2019, 19:14
Expert's post
sandy wrote:
\(x^2 > y^2\) and \(x > -|y|\)

Quantity A
Quantity B
x
y


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.


\(x^2>y^2\) means \(|x|>|y|\)..
This means x is farther away from 0 as compared to y..
So there can be four ways...
x....y....0
X.............0....y
0....y....x
y....0.............x

So if x>0 then x>y , but if x<0, then x<y...
So the relationship depend on the SIGN of x..

Now next we are given x>-|y|
Let us check the four cases
x....y....0. => If x<0 then x>-|y| is not true as -|y| >0.
X..........0....y => If x<0 then x>-|y| is not true as -|y| <0, but -|y| will be closer to 0.
0....y....x => If x>0 then x>-|y| is possible.
y....0..........x => If x<0 then x>-|y| is again possible..

In both the cases that are possible, x>y..

Hence A
_________________

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

Re: x2 > y2 and x > –|y|   [#permalink] 02 Jan 2019, 19:14
Display posts from previous: Sort by

x2 > y2 and x > –|y|

  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®.