November 17, 2018 November 17, 2018 07:00 AM PST 09:00 AM PST Nov. 17, 7 AM PST. Aiming to score 760+? Attend this FREE session to learn how to Define your GMAT Strategy, Create your Study Plan and Master the Core Skills to excel on the GMAT. November 17, 2018 November 17, 2018 09:00 AM PST 11:00 AM PST Join the Quiz Saturday November 17th, 9 AM PST. The Quiz will last approximately 2 hours. Make sure you are on time or you will be at a disadvantage.
Author 
Message 
TAGS:

Hide Tags

Senior Manager
Status: Do and Die!!
Joined: 15 Sep 2010
Posts: 271

If x and y are integers and xy 0, is x  y > 0 ?
[#permalink]
Show Tags
Updated on: 11 Apr 2014, 02:45
Question Stats:
64% (01:45) correct 36% (01:43) wrong based on 98 sessions
HideShow timer Statistics
If x and y are integers and xy ≠ 0, is x  y > 0 ? (1) x/y < 1/2 (2) \(\sqrt{x^2}=x\) and \(\sqrt{y^2}=y\) Why I alone isn't sufficient , since x/y <1/2 => x<y/2 .. As X is even less than half of Y so X can't be greater than Y
Official Answer and Stats are available only to registered users. Register/ Login.
_________________
I'm the Dumbest of All !!
Originally posted by shrive555 on 27 Oct 2010, 17:38.
Last edited by Bunuel on 11 Apr 2014, 02:45, edited 1 time in total.
Edited the question



Math Expert
Joined: 02 Sep 2009
Posts: 50619

Re: integers x & y
[#permalink]
Show Tags
27 Oct 2010, 17:52
shrive555 wrote: If x and y are integers and xy ≠ 0, is x  y > 0 ?
1  x/y <1/2
2 sqr X^2 = X and sqr Y^2 = Y
Why I alone isn't sufficient , since x/y <1/2 => x<y/2 .. As X is even less than half of Y so X can't be greater than Y Question: is \(x>y\)? (1) \(\frac{x}{y}<\frac{1}{2}\) > if both \(x\) and \(y\) are positive (for example 1 and 3 respectively) then \(x<y\) and the answer to the question is NO but if \(x\) and \(y\) are both negative (for example 1 and 3 respectively) then \(x>y\) and the answer to the question is YES. Not sufficient. (2) \(\sqrt{x^2}=x\) and \(\sqrt{y^2}=y\) > both \(x\) and \(y\) are positive (as square root function can not give negative result and we know that neither of unknown is zero), but we don't know whether \(x>y\). Not sufficient. (1)+(2) From (2) both \(x\) and \(y\) are positive so from (1) \(x<y\) and the answer to the question is NO. Sufficient. Answer: C. As for your solution: red part is not correct. You can not multiply inequality by y as you don't know the sign of it. Never multiply or reduce inequality by an unknown (a variable) unless you are sure of its sign since you do not know whether you must flip the sign of the inequality.Hope it helps.
_________________
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? Extrahard Quant Tests with Brilliant Analytics



Senior Manager
Status: Do and Die!!
Joined: 15 Sep 2010
Posts: 271

Re: integers x & y
[#permalink]
Show Tags
27 Oct 2010, 18:37
....Great Point to remember !!! +2
_________________
I'm the Dumbest of All !!



Manager
Status: Will Retake GMAT
Joined: 29 Jul 2010
Posts: 102
Location: India
Concentration: General Management, Entrepreneurship
GPA: 3.11
WE: Information Technology (Computer Software)

Re: integers x & y
[#permalink]
Show Tags
27 Oct 2010, 23:52
Really good one Bunuel... thanks
_________________
Retaking GMAT. Hope the charm works this time..



Intern
Joined: 01 Aug 2006
Posts: 33

Re: If x and y are integers and xy 0, is x  y > 0 ?
[#permalink]
Show Tags
07 Feb 2014, 07:17
x and y are nonzero integers. Is x > y? 1. x/y < 1/2 > x = 1 , y = 8, NO. x = 1, y = 8, YES. 2. x = x and y = y; x and y are both positive. but x > y and x < y possible. Remember Sqrt(x^2) = x and NOT x.
Combining, x and y are positive and x < y/2 => x < y.
C



Director
Joined: 27 May 2012
Posts: 609

Re: If x and y are integers and xy 0, is x  y > 0 ?
[#permalink]
Show Tags
10 Apr 2014, 02:43
shrive555 wrote: If x and y are integers and xy ≠ 0, is x  y > 0 ?
(1) x/y < 1/2 (2) \(\sqrt{x^2}=x\)
Why I alone isn't sufficient , since x/y <1/2 => x<y/2 .. As X is even less than half of Y so X can't be greater than Y Please note some how statement 2 has been edited , part of statement 2 is missing, \(sqrt (y^2) = y\), should be there. The question as given now , gives answer as E. Hope concerned persons will look into this. Thank you.
_________________
 Stne



Intern
Joined: 08 Apr 2014
Posts: 12

Re: If x and y are integers and xy 0, is x  y > 0 ?
[#permalink]
Show Tags
10 Apr 2014, 04:57
stne wrote: shrive555 wrote: If x and y are integers and xy ≠ 0, is x  y > 0 ?
(1) x/y < 1/2 (2) \(\sqrt{x^2}=x\)
Why I alone isn't sufficient , since x/y <1/2 => x<y/2 .. As X is even less than half of Y so X can't be greater than Y Please note some how statement 2 has been edited , part of statement 2 is missing, \(sqrt (y^2) = y\), should be there. The question as given now , gives answer as E. Hope concerned persons will look into this. Thank you. Hi Stne, We do not really need \(sqrt (y^2) = y\) because if \(\sqrt{x^2}=x\) is true, x is positive and as x/y < 1/2 => 2x < y Hence as y is greater than 2x, it has to be positive. * press Kudos if you like the post!



Director
Joined: 27 May 2012
Posts: 609

Re: If x and y are integers and xy 0, is x  y > 0 ?
[#permalink]
Show Tags
10 Apr 2014, 07:05
ricsingh wrote: stne wrote: shrive555 wrote: If x and y are integers and xy ≠ 0, is x  y > 0 ?
(1) x/y < 1/2 (2) \(\sqrt{x^2}=x\)
Why I alone isn't sufficient , since x/y <1/2 => x<y/2 .. As X is even less than half of Y so X can't be greater than Y Please note some how statement 2 has been edited , part of statement 2 is missing, \(sqrt (y^2) = y\), should be there. The question as given now , gives answer as E. Hope concerned persons will look into this. Thank you. Hi Stne, We do not really need \(sqrt (y^2) = y\) because if \(\sqrt{x^2}=x\) is true, x is positive and as x/y < 1/2 => 2x < y Hence as y is greater than 2x, it has to be positive. * press Kudos if you like the post!You cannot cross multiply in inequality without knowing the signs of x and y , you can cross multiply only when you know that the signs are positive if the question does not have \(sqrt (y^2) = y\) then y need not necessarily be positive consider x=1 and y = 3 this satisfies both the statement and the answer is no consider x= 1 and y = 3 this satisfies both the statements and the answer is yes as you can see, Y has to be positive for the answer to be c . Hence question should be corrected, as in the present format, answer is E Hope it helps , let me know if there is anything still unclear.
_________________
 Stne



Intern
Joined: 08 Apr 2014
Posts: 12

Re: If x and y are integers and xy 0, is x  y > 0 ?
[#permalink]
Show Tags
10 Apr 2014, 07:44
stne wrote: ricsingh wrote: shrive555 wrote: If x and y are integers and xy ≠ 0, is x  y > 0 ?
(1) x/y < 1/2 (2) \(\sqrt{x^2}=x\)
Why I alone isn't sufficient , since x/y <1/2 => x<y/2 .. As X is even less than half of Y so X can't be greater than Y Please note some how statement 2 has been edited , part of statement 2 is missing, \(sqrt (y^2) = y\), should be there. The question as given now , gives answer as E. Hope concerned persons will look into this. Thank you. Hi Stne, We do not really need \(sqrt (y^2) = y\) because if \(\sqrt{x^2}=x\) is true, x is positive and as x/y < 1/2 => 2x < y Hence as y is greater than 2x, it has to be positive. * press Kudos if you like the post!You cannot cross multiply in inequality without knowing the signs of x and y , you can cross multiply only when you know that the signs are positive if the question does not have \(sqrt (y^2) = y\) then y need not necessarily be positive consider x=1 and y = 3 this satisfies both the statement and the answer is no consider x= 1 and y = 3 this satisfies both the statements and the answer is yes as you can see, Y has to be positive for the answer to be c . Hence question should be corrected, as in the present format, answer is E Hope it helps , let me know if there is anything still unclear.[/quote] But, incase y is negative: x y will always be greater than 0, given x is positive and x & y are nonzero integers. For example 1 (3) > 0 *press Kudos if you like the post!



Director
Joined: 27 May 2012
Posts: 609

Re: If x and y are integers and xy 0, is x  y > 0 ?
[#permalink]
Show Tags
10 Apr 2014, 10:59
Hi Ricsingh, x= 1 and y = 3 what is xy ? its 2 so is x y >0 answer No. x=1 and y = 3 what is x y ? its 4 so is xy >0 answer yes So what is the confusion? we have two different answers if \(sqrt(y^2)= y\) is not given. So it is very important to mention that Y is positive. Hope this will help, if any thing is still unclear .let me know
_________________
 Stne



Intern
Joined: 10 Apr 2014
Posts: 33

Re: If x and y are integers and xy 0, is x  y > 0 ?
[#permalink]
Show Tags
10 Apr 2014, 13:04
stne wrote: Hi Ricsingh,
x= 1 and y = 3 what is xy ? its 2 so is x y >0 answer No. x=1 and y = 3 what is x y ? its 4 so is xy >0 answer yes
So what is the confusion? we have two different answers if \(sqrt(y^2)= y\) is not given. So it is very important to mention that Y is positive.
Hope this will help, if any thing is still unclear .let me know Hello  I agree that we need to know Y is positive or not for this question and I think someone has corrected it as well. Just a thought, if we know Y is positive we do not really need to know what X is to answer the question. because when x is negative xy > 0 , not true when x is positive, xy >0 , not true if x is less than y and first statement confirms that. Letme know your thoughts on this.



NonHuman User
Joined: 09 Sep 2013
Posts: 8791

Re: If x and y are integers and xy 0, is x  y > 0 ?
[#permalink]
Show Tags
15 Oct 2017, 11:01
Hello from the GMAT Club BumpBot! Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up  doing my job. I think you may find it valuable (esp those replies with Kudos). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
GMAT Books  GMAT Club Tests  Best Prices on GMAT Courses  GMAT Mobile App  Math Resources  Verbal Resources




Re: If x and y are integers and xy 0, is x  y > 0 ? &nbs
[#permalink]
15 Oct 2017, 11:01






