Author 
Message 
TAGS:

Hide Tags

Manager
Joined: 25 Jul 2012
Posts: 75
Location: United States

Is xy > x^2*y^2 ? [#permalink]
Show Tags
17 Aug 2013, 12:51
2
This post received KUDOS
16
This post was BOOKMARKED
Question Stats:
76% (02:10) correct
24% (01:15) wrong based on 515 sessions
HideShow timer Statistics
Is xy > x^2*y^2 ? (1) 0 < x^2 < 1/4 (2) 0 < y^2 < 1/9 Source: GMAT Prep Question Pack 1 Difficulty: Medium  Can someone please explain what to do with xy > x^2y^2 before we look into the equations?
I got xy > (xy)^2 but I didn't know how to interpret the inequality from here. Thanks in advance
Official Answer and Stats are available only to registered users. Register/ Login.
_________________
If my post has contributed to your learning or teaching in any way, feel free to hit the kudos button ^_^



Director
Joined: 14 Dec 2012
Posts: 832
Location: India
Concentration: General Management, Operations
GPA: 3.6

Re: Is xy > x^2*y^2 ? [#permalink]
Show Tags
17 Aug 2013, 13:01
3
This post received KUDOS
3
This post was BOOKMARKED
DelSingh wrote: xy > x^2y^2 ?
1) 0 < x^2 < 1/4
2) 0 < y^2 < 1/9
IMO C \(xy > x^2y^2\) since both sides are positive square both sides \((xy)^2 > (xy)^4\) \((xy)^2((xy)^21)<0\) since \((xy)^2>0\) therefore \((xy)^21<0\) \((xy)^2<1\) or 1<xy<1 ......so finally this is question. finally you need both x and y to come to conclusion STATEMENT 1==>ONLY X HENCE INSUFFICIENT. \(0 < x^2 < 1/4\) \(1/2<x<1/2\) STATEMENT 2 ==>ONLY Y HENCE INSUFFICIENT \(0 < y^2 < 1/9\) \(1/3<y<1/3\) now combining both clearly \(1<xy<1\) hence CHOPE IT HELPS
_________________
When you want to succeed as bad as you want to breathe ...then you will be successfull....
GIVE VALUE TO OFFICIAL QUESTIONS...
GMAT RCs VOCABULARY LIST: http://gmatclub.com/forum/vocabularylistforgmatreadingcomprehension155228.html learn AWA writing techniques while watching video : http://www.gmatprepnow.com/module/gmatanalyticalwritingassessment : http://www.youtube.com/watch?v=APt9ITygGss
Last edited by blueseas on 17 Aug 2013, 15:16, edited 1 time in total.



Manager
Joined: 04 Apr 2013
Posts: 150

Re: Is xy > x^2*y^2 ? [#permalink]
Show Tags
17 Aug 2013, 14:45
blueseas wrote: DelSingh wrote: xy > x^2y^2 ?
1) 0 < x^2 < 1/4
2) 0 < y^2 < 1/9
\(xy > x^2y^2\) since both sides are positive square both sides \((xy)^2 > (xy)^4\) \((xy)^2((xy)^21)<0\) since \((xy)^2>0\) therefore \((xy)^21<0\) \((xy)^2<1\) ......so finally this is question. finally you need both x and y to come to conclusion STATEMENT 1==>ONLY X HENCE INSUFFICIENT. STATEMENT 2 ==>ONLY Y HENCE INSUFFICIENT hence DHOPE IT HELPS If both are insufficient OA is either C or E. Could you please elaborate? for me the OA is C Case 1: > 1/2 < x < 1/2 and x <> 0 we dont know if xy>x^2y^2 as we dont know about Y case 2; > 1/3 < y < 1/3 and y <> 0 we dont know if xy>x^2y^2 as we dont know about X Combining both for any values of x & Y , xy > x^2y^2
_________________
Maadhu
MGMAT1  540 ( Trying to improve )



Director
Joined: 14 Dec 2012
Posts: 832
Location: India
Concentration: General Management, Operations
GPA: 3.6

Re: Is xy > x^2*y^2 ? [#permalink]
Show Tags
17 Aug 2013, 15:17
1
This post received KUDOS
maaadhu wrote:
If both are insufficient OA is either C or E. Could you please elaborate?
for me the OA is C
THANKS . that was mistake.
_________________
When you want to succeed as bad as you want to breathe ...then you will be successfull....
GIVE VALUE TO OFFICIAL QUESTIONS...
GMAT RCs VOCABULARY LIST: http://gmatclub.com/forum/vocabularylistforgmatreadingcomprehension155228.html learn AWA writing techniques while watching video : http://www.gmatprepnow.com/module/gmatanalyticalwritingassessment : http://www.youtube.com/watch?v=APt9ITygGss



Director
Joined: 25 Apr 2012
Posts: 728
Location: India
GPA: 3.21
WE: Business Development (Other)

Is xy>x^2y^2 [#permalink]
Show Tags
24 Jul 2014, 20:33
Q. \(Is xy>x^{2}y^{2}\) 1.\(0<x^{2}<1/4\) 2. \(0<y^{2}<1/9\) In the answer explanation, the question is boiled down to is x^2 *y^2< 1.. Where as I solved it by saying that since x^2/geq{0} and y^2/geq{0} and thus not equal to zero the expression is true..I don't see a reason to prove less than 1 because if value of x and y are less than 1 then surely x^2y^2 will be less than 1...am I correct ??
_________________
“If you can't fly then run, if you can't run then walk, if you can't walk then crawl, but whatever you do you have to keep moving forward.”



Manager
Joined: 21 Jul 2014
Posts: 127

Re: Is xy>x^2y^2 [#permalink]
Show Tags
24 Jul 2014, 20:49
7
This post received KUDOS
Here, it helps to know that numbers greater than 1, when squared, are larger. Numbers between 0 and 1, when squared, are smaller.
Once you establish that, you're just saying:
Statement 1: x^2 = smaller; y^2 = unknown (smaller or large) ==> Don't know if product is larger or smaller because you don't know magnitude Statement 2: y^2 = smaller; x^2 = unknkown (smaller or larger) ==> Don't know if product is larger or smaller because you don't know magnitude
Statement 1 and 2: x^2 = smaller; y^2 = smaller ==> product is smaller because both numbers are smaller.
Therefore, correct answer is (C).



Intern
Joined: 03 Jul 2013
Posts: 35

Re: Is xy>x^2y^2 [#permalink]
Show Tags
24 Jul 2014, 21:00
I will go with C .
 xy  is a positive and x^2 y^2 must be positive . x and y are positives or negatives . it does not matter . Only way to satisfy the condition is that both X & Y must be fractions .
basically we are asked that whether both x and y are fraction ?
1) it tells us x is a fraction because the highest possible value of x can be 1/2 . no info about y hence not sufficient.
2) it tells us , y is a fraction but no info about x . not sufficient
(1) + (2) , now both x & y are fractions so
 xy  will always be greater than x ^2 y ^2 .
hence sufficient . so answer is C
Posted from my mobile device



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 7453
Location: Pune, India

Re: Is xy>x^2y^2 [#permalink]
Show Tags
24 Jul 2014, 22:39
7
This post received KUDOS
Expert's post
10
This post was BOOKMARKED
WoundedTiger wrote: Q. \(Is xy>x^{2}y^{2}\) 1.\(0<x^{2}<1/4\) 2. \(0<y^{2}<1/9\) In the answer explanation, the question is boiled down to is x^2 *y^2< 1.. Where as I solved it by saying that since x^2/geq{0} and y^2/geq{0} and thus not equal to zero the expression is true..I don't see a reason to prove less than 1 because if value of x and y are less than 1 then surely x^2y^2 will be less than 1...am I correct ?? Two variables are confusing you. Note that the question is just this: Is \(xy> x^{2}y^{2}\) Is \(xy> xy^2\) Is \(z > z^2\) where \(z = xy\) When is z greater than z^2? When z lies between 1 and 1 or we can say between 0 and 1 when z is positive. 1.\(0<x^{2}<1/4\) This tells you that 0 < x < 1/2. Doesn't tell you anything about y so you don't know anything about z. 2. \(0<y^{2}<1/9\) This tells you that 0 < y < 1/3. Doesn't tell you anything about x so you don't know anything about z. Both together, you know that x*y is less than 1 i.e. z is less than 1. Hence z WILL BE greater than z^2. Answer (C)
_________________
Karishma Veritas Prep  GMAT Instructor My Blog
Get started with Veritas Prep GMAT On Demand for $199
Veritas Prep Reviews



Math Expert
Joined: 02 Sep 2009
Posts: 39759

Re: Is xy > x^2*y^2 ? [#permalink]
Show Tags
25 Jul 2014, 00:28
1
This post received KUDOS
Expert's post
1
This post was BOOKMARKED



Manager
Joined: 11 Sep 2013
Posts: 152
Concentration: Finance, Finance

Re: GMAT prep question pack 1 [#permalink]
Show Tags
18 Aug 2014, 23:26
If (xy)^2 is positive, (xy)^2>(xy)4 or 1> (xy)^2 I and 2 are insufficient because in each statement other value is missing.
By combining We know that (xy)^2 is positive. So,
(xy)^2< (1/4)*(1/9) Clearly, 1> (xy)^2 Is my reasoning correct? Need expert help



GMAT Club Legend
Joined: 09 Sep 2013
Posts: 16036

Re: Is xy > x^2*y^2 ? [#permalink]
Show Tags
24 Aug 2015, 05:44
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



Intern
Joined: 15 Dec 2015
Posts: 44

Re: Is xy > x^2*y^2 ? [#permalink]
Show Tags
15 Dec 2015, 02:31
VeritasPrepKarishma wrote: When is z greater than z^2? When z lies between 1 and 1 VeritasPrepKarishma : Except for z=0 right?



Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 3480
GPA: 3.82

Re: Is xy > x^2*y^2 ? [#permalink]
Show Tags
15 Dec 2015, 22:15
Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution. Is xy > x^2*y^2 ? (1) 0 < x^2 < 1/4 (2) 0 < y^2 < 1/9 When you modify the original condition and the problem, xy>xy^2?, 0>xy^2xy?, 0>xy(xy1)?. That is, 0<xy<1? > xy=/0 and 1<xy<1?. There are 2 variables(x,y), which should match with the number of equations. So, you need 2 more equations. For 1) 1 equation, for 2) 1 equation, which is likely to make c the answer. In 1)&2), x=/0 and 1/2<x<1/2, y=/0 and 1/3<y<1/3, xy=/0 and 1/6<xy<1/6, which is always yes and sufficient. Therefore, the answer is C. > For cases where we need 2 more equations, such as original conditions with “2 variables”, or “3 variables and 1 equation”, or “4 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 70% chance that C is the answer, while E has 25% chance. These two are the majority. In case of common mistake type 3,4, the answer may be from A, B or D but there is only 5% chance. Since C is most likely to be the answer using 1) and 2) separately according to DS definition (It saves us time). Obviously there may be cases where the answer is A, B, D or E.
_________________
MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The oneandonly World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. Find a 10% off coupon code for GMAT Club members. “Receive 5 Math Questions & Solutions Daily” Unlimited Access to over 120 free video lessons  try it yourself See our Youtube demo



GMAT Club Legend
Joined: 09 Sep 2013
Posts: 16036

Re: Is xy > x^2*y^2 ? [#permalink]
Show Tags
14 Feb 2017, 11:03
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: Is xy > x^2*y^2 ?
[#permalink]
14 Feb 2017, 11:03







