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

It is currently 21 Oct 2018, 20:35

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

Is x > y ? (1) ax > ay (2) a^2 * x > a^2 * y

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

Hide Tags

Senior Manager
Senior Manager
User avatar
Joined: 20 Mar 2008
Posts: 430
Is x > y ? (1) ax > ay (2) a^2 * x > a^2 * y  [#permalink]

Show Tags

New post Updated on: 14 Apr 2012, 01:52
6
00:00
A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

69% (01:00) correct 31% (00:55) wrong based on 271 sessions

HideShow timer Statistics

Is x > y ?

(1) ax > ay
(2) a^2 * x > a^2 * y

Originally posted by Jivana on 10 Aug 2009, 18:21.
Last edited by Bunuel on 14 Apr 2012, 01:52, edited 1 time in total.
Edited the question and added the OA
Manager
Manager
avatar
Joined: 10 Jul 2009
Posts: 143
Re: Is x > y ?  [#permalink]

Show Tags

New post 10 Aug 2009, 18:57
3
1
1. ax > ay. The inequality between x and y depends on a, which can be either positive or negative.

2. a^2.x > a^2.y
Though a is positive or negative a^2 will always be positive.
So we can conclude x > y.
2 alone is sufficient, where as 1 alone is not sufficient.
So answer is B
Retired Moderator
User avatar
B
Joined: 05 Jul 2006
Posts: 1727
GMAT ToolKit User Premium Member
Re: Is x > y ?  [#permalink]

Show Tags

New post 10 Aug 2009, 23:09
1
Is x > y ?

(1) ax > ay
(2) a^2 . x > a^2 . y

from 1

ax-ay>0

a(x-y)>0 we dont know whether a is -ve or +ve...insuff

from 2

a^2(x-y)>0 a^2 is +ve thus x-y is +ve thus x>y...suff

B
Manager
Manager
avatar
Status: Applying
Joined: 19 Jul 2009
Posts: 120
Location: United Kingdom
Concentration: General Management, Strategy
GPA: 3.65
WE: Consulting (Telecommunications)
Re: Is x > y ?  [#permalink]

Show Tags

New post 10 Aug 2009, 23:14
B it is ...

by squaring 'a' you are making it +ve ....
Intern
Intern
avatar
Joined: 30 Jan 2011
Posts: 18
Re: Is x > y ?  [#permalink]

Show Tags

New post 11 Jul 2011, 17:02
Statement 1: If a is negative and we divide both side of the inequality by a, then the order of the inequality reverses: x < y
If a is positive --> x > y
==> INSUFF.

Statement 2: SUFF.
Intern
Intern
avatar
Joined: 13 Apr 2012
Posts: 1
GMAT ToolKit User
Re: Is x > y ?  [#permalink]

Show Tags

New post 13 Apr 2012, 20:52
AshForGMAT wrote:
B it is ...

by squaring 'a' you are making it +ve ....



What if a=sqrt(-1)?
a^2 will then be negative. I've seen another gmat question where it's tricky like that.

Image Posted from GMAT ToolKit
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 50009
Re: Is x > y ?  [#permalink]

Show Tags

New post 14 Apr 2012, 02:02
Avh86 wrote:
AshForGMAT wrote:
B it is ...

by squaring 'a' you are making it +ve ....



What if a=sqrt(-1)?
a^2 will then be negative. I've seen another gmat question where it's tricky like that.

Image Posted from GMAT ToolKit


Welcome to GMAT Club. Below is an answer to your question.

First of all, the GMAT is dealing only with Real Numbers, so even roots from negative numbers are not defined. So, \(a^{even}\geq{0}\).

Is x>y?

Question: is \(x-y> 0\)

(1) \(ax>ay\) --> \(a(x-y)>0\), two cases:
A. \(a>0\) and \(x-y>0\);
OR
B. \(a<0\) and \(x-y<0\);
Depending on \(a\), \(x-y\) may or may not be greater than zero. Not sufficient.

(2) \(a^2x > a^2y\) --> \(a^2(x-y)>0\) --> since \(a^2>0\) (\(a^2\) can not be zero, since the product is more than zero) we can safely reduce by it: \(x-y>0\). Sufficient.

Answer: B.

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

Manager
Manager
avatar
Status: I will not stop until i realise my goal which is my dream too
Joined: 25 Feb 2010
Posts: 196
Schools: Johnson '15
Re: Is x > y ? (1) ax > ay (2) a^2 * x > a^2 * y  [#permalink]

Show Tags

New post 14 Apr 2012, 21:50
Jivana wrote:
Is x > y ?

(1) ax > ay
(2) a^2 * x > a^2 * y



Explanation:

1: AX > AY
no mention of whether A, X & Y are +ve or -ve....
so A = -ve
X = -ve
Y = -ve
two conditions arise
X< Y, AX> AY
X>Y, AX> Ay
hence Not sufficient

2. A2 * X > A2 * Y
so X> Y irrespective of a2 values...
hence SUFFICIENT
_________________

Regards,
Harsha

Note: Give me kudos if my approach is right , else help me understand where i am missing.. I want to bell the GMAT Cat ;)

Satyameva Jayate - Truth alone triumphs

Intern
Intern
avatar
Joined: 02 Oct 2013
Posts: 12
Re: Is x > y ?  [#permalink]

Show Tags

New post 25 Oct 2013, 00:29
Bunuel wrote:
Avh86 wrote:
AshForGMAT wrote:
B it is ...

by squaring 'a' you are making it +ve ....



What if a=sqrt(-1)?
a^2 will then be negative. I've seen another gmat question where it's tricky like that.

Image Posted from GMAT ToolKit


Welcome to GMAT Club. Below is an answer to your question.


First of all, the GMAT is dealing only with Real Numbers, so even roots from negative numbers are not defined. So, \(a^{even}\geq{0}\).

Is x>y?

Question: is \(x-y> 0\)

(1) \(ax>ay\) --> \(a(x-y)>0\), two cases:
A. \(a>0\) and \(x-y>0\);
OR
B. \(a<0\) and \(x-y<0\);
Depending on \(a\), \(x-y\) may or may not be greater than zero. Not sufficient.

(2) \(a^2x > a^2y\) --> \(a^2(x-y)>0\) --> since \(a^2>0\) (\(a^2\) can not be zero, since the product is more than zero) we can safely reduce by it: \(x-y>0\). Sufficient.

Answer: B.

Hope it's clear.



Hi Bunuel

What if question is

Is x = y

A) ax = bx
B ) a^2x = a^2y

Would then the answer be D

Regards
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 50009
Re: Is x > y ?  [#permalink]

Show Tags

New post 25 Oct 2013, 01:55
DivyanshuRohatgi wrote:
Bunuel wrote:
Avh86 wrote:


What if a=sqrt(-1)?
a^2 will then be negative. I've seen another gmat question where it's tricky like that.

Image Posted from GMAT ToolKit


Welcome to GMAT Club. Below is an answer to your question.


First of all, the GMAT is dealing only with Real Numbers, so even roots from negative numbers are not defined. So, \(a^{even}\geq{0}\).

Is x>y?

Question: is \(x-y> 0\)

(1) \(ax>ay\) --> \(a(x-y)>0\), two cases:
A. \(a>0\) and \(x-y>0\);
OR
B. \(a<0\) and \(x-y<0\);
Depending on \(a\), \(x-y\) may or may not be greater than zero. Not sufficient.

(2) \(a^2x > a^2y\) --> \(a^2(x-y)>0\) --> since \(a^2>0\) (\(a^2\) can not be zero, since the product is more than zero) we can safely reduce by it: \(x-y>0\). Sufficient.

Answer: B.

Hope it's clear.



Hi Bunuel

What if question is

Is x = y

A) ax = bx
B ) a^2x = a^2y

Would then the answer be D

Regards


No, in this case the answer would be E. Consider: x=y=0 or a=b=0.
_________________

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
B
Joined: 09 Jul 2017
Posts: 11
Location: India
GPA: 3.66
WE: Marketing (Real Estate)
CAT Tests
Is x>y?  [#permalink]

Show Tags

New post 28 May 2018, 20:09
Is x>y?

A) ax>ay
B) a^2x>a^2y
Math Expert
User avatar
V
Joined: 02 Aug 2009
Posts: 6975
Re: Is x>y?  [#permalink]

Show Tags

New post 28 May 2018, 20:14
1
shruti.shambhavi wrote:
Is x>y?

A) ax>ay
B) a^2x>a^2y



A) ax>ay...
If a is positive, yes otherwise no
Insufficient
B) \(a^2x>a^2y....x>y\)
Sufficient

B
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html


GMAT online Tutor

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 50009
Re: Is x > y ? (1) ax > ay (2) a^2 * x > a^2 * y  [#permalink]

Show Tags

New post 28 May 2018, 23:44
GMAT Club Bot
Re: Is x > y ? (1) ax > ay (2) a^2 * x > a^2 * y &nbs [#permalink] 28 May 2018, 23:44
Display posts from previous: Sort by

Is x > y ? (1) ax > ay (2) a^2 * x > a^2 * y

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


cron
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®.