Find all School-related info fast with the new School-Specific MBA Forum

It is currently 28 Apr 2016, 15:49
GMAT Club 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.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

Is |xy| > x^2*y^2 ?

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

2 KUDOS received
Manager
Manager
avatar
Joined: 25 Jul 2012
Posts: 78
Location: United States
Followers: 0

Kudos [?]: 63 [2] , given: 137

Is |xy| > x^2*y^2 ? [#permalink]

Show Tags

New post 17 Aug 2013, 12:51
2
This post received
KUDOS
10
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  5% (low)

Question Stats:

75% (02:15) correct 25% (01:14) wrong based on 345 sessions

HideShow timer Statictics

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

--------------------
[Reveal] Spoiler:
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
[Reveal] Spoiler: OA

_________________

If my post has contributed to your learning or teaching in any way, feel free to hit the kudos button ^_^

2 KUDOS received
Director
Director
User avatar
Joined: 14 Dec 2012
Posts: 842
Location: India
Concentration: General Management, Operations
GMAT 1: 700 Q50 V34
GPA: 3.6
Followers: 49

Kudos [?]: 977 [2] , given: 197

GMAT ToolKit User
Re: Is |xy| > x^2*y^2 ? [#permalink]

Show Tags

New post 17 Aug 2013, 13:01
2
This post received
KUDOS
2
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
\((xy)^2 > (xy)^4\)
\((xy)^2((xy)^2-1)<0\)
since \((xy)^2>0\) therefore \((xy)^2-1<0\)
\((xy)^2<1\)
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 C

HOPE 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: vocabulary-list-for-gmat-reading-comprehension-155228.html
learn AWA writing techniques while watching video : http://www.gmatprepnow.com/module/gmat- ... assessment
: http://www.youtube.com/watch?v=APt9ITygGss


Last edited by blueseas on 17 Aug 2013, 15:16, edited 1 time in total.
Manager
Manager
avatar
Joined: 04 Apr 2013
Posts: 153
Followers: 1

Kudos [?]: 36 [0], given: 36

Re: Is |xy| > x^2*y^2 ? [#permalink]

Show Tags

New post 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
\((xy)^2 > (xy)^4\)
\((xy)^2((xy)^2-1)<0\)
since \((xy)^2>0\) therefore \((xy)^2-1<0\)
\((xy)^2<1\)
......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 D

HOPE 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 )

1 KUDOS received
Director
Director
User avatar
Joined: 14 Dec 2012
Posts: 842
Location: India
Concentration: General Management, Operations
GMAT 1: 700 Q50 V34
GPA: 3.6
Followers: 49

Kudos [?]: 977 [1] , given: 197

GMAT ToolKit User
Re: Is |xy| > x^2*y^2 ? [#permalink]

Show Tags

New post 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: vocabulary-list-for-gmat-reading-comprehension-155228.html
learn AWA writing techniques while watching video : http://www.gmatprepnow.com/module/gmat- ... assessment
: http://www.youtube.com/watch?v=APt9ITygGss

Moderator
Moderator
User avatar
Joined: 25 Apr 2012
Posts: 728
Location: India
GPA: 3.21
WE: Business Development (Other)
Followers: 41

Kudos [?]: 562 [0], given: 723

Premium Member Reviews Badge
Is |xy|>x^2y^2 [#permalink]

Show Tags

New post 24 Jul 2014, 20:33
Q. \(Is |xy|>x^{2}y^{2}\)

1.\(0<x^{2}<1/4\)
2. \(0<y^{2}<1/9\)

[Reveal] Spoiler:
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.”

2 KUDOS received
Manager
Manager
User avatar
Joined: 21 Jul 2014
Posts: 127
Followers: 4

Kudos [?]: 107 [2] , given: 12

GMAT ToolKit User
Re: Is |xy|>x^2y^2 [#permalink]

Show Tags

New post 24 Jul 2014, 20:49
2
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
Intern
avatar
Joined: 03 Jul 2013
Posts: 36
Followers: 2

Kudos [?]: 15 [0], given: 0

GMAT ToolKit User
Re: Is |xy|>x^2y^2 [#permalink]

Show Tags

New post 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 Image
Expert Post
5 KUDOS received
Veritas Prep GMAT Instructor
User avatar
Joined: 16 Oct 2010
Posts: 6467
Location: Pune, India
Followers: 1750

Kudos [?]: 10445 [5] , given: 205

Re: Is |xy|>x^2y^2 [#permalink]

Show Tags

New post 24 Jul 2014, 22:39
5
This post received
KUDOS
Expert's post
5
This post was
BOOKMARKED
WoundedTiger wrote:
Q. \(Is |xy|>x^{2}y^{2}\)

1.\(0<x^{2}<1/4\)
2. \(0<y^{2}<1/9\)

[Reveal] Spoiler:
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

Expert Post
1 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 32508
Followers: 5620

Kudos [?]: 68150 [1] , given: 9797

Re: Is |xy| > x^2*y^2 ? [#permalink]

Show Tags

New post 25 Jul 2014, 00:28
1
This post received
KUDOS
Expert's post
1
This post was
BOOKMARKED
WoundedTiger wrote:
Q. \(Is |xy|>x^{2}y^{2}\)

1.\(0<x^{2}<1/4\)
2. \(0<y^{2}<1/9\)

[Reveal] Spoiler:
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 ??

_________________
Merging topics.
_________________

New to the Math Forum?
Please read this: 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
User avatar
Joined: 11 Sep 2013
Posts: 153
Concentration: Finance, Finance
Followers: 2

Kudos [?]: 56 [0], given: 156

Re: GMAT prep question pack 1 [#permalink]

Show Tags

New post 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
GMAT Club Legend
User avatar
Joined: 09 Sep 2013
Posts: 9201
Followers: 453

Kudos [?]: 114 [0], given: 0

Premium Member
Re: Is |xy| > x^2*y^2 ? [#permalink]

Show Tags

New post 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
Intern
avatar
Joined: 15 Dec 2015
Posts: 22
Followers: 0

Kudos [?]: 0 [0], given: 14

Re: Is |xy| > x^2*y^2 ? [#permalink]

Show Tags

New post 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?
Expert Post
Math Revolution GMAT Instructor
User avatar
Joined: 16 Aug 2015
Posts: 1043
GPA: 3.82
Followers: 61

Kudos [?]: 443 [0], given: 0

Premium Member
Re: Is |xy| > x^2*y^2 ? [#permalink]

Show Tags

New post 15 Dec 2015, 22:15
Expert's post
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|^2-|xy|?, 0>|xy|(|xy|-1)?. 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 one-and-only 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.
Unlimited Access to over 120 free video lessons - try it yourself
See our Youtube demo

Re: Is |xy| > x^2*y^2 ?   [#permalink] 15 Dec 2015, 22:15
    Similar topics Author Replies Last post
Similar
Topics:
Experts publish their posts in the topic Is |x^2+y^2| > |x^2-y^2|? Bunuel 0 24 Sep 2015, 01:53
2 Is |XY| > X^2Y^2? alexa 1 08 Oct 2014, 17:39
15 Experts publish their posts in the topic Is |x^2 + y^2| > |x^2 - y^2|? makhija1 21 04 Jun 2013, 20:45
12 Experts publish their posts in the topic Is x^4 + y^4 > z^4 ? (1) x^2 + y^2 > z^2 (2) x+y > dungtd 9 30 Jul 2010, 12:54
6 Experts publish their posts in the topic Is xy > x^2*y^2? (1) 14*x^2 = 3 (2) y^2 = 1 jade3 11 24 Nov 2009, 21:56
Display posts from previous: Sort by

Is |xy| > x^2*y^2 ?

  Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group and phpBB SEO

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®.