It is currently 18 Nov 2017, 22:18

### 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

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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

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

Author Message
TAGS:

### Hide Tags

Manager
Joined: 25 Jul 2012
Posts: 73

Kudos [?]: 120 [4], given: 137

Location: United States
Is |xy| > x^2*y^2 ? [#permalink]

### Show Tags

17 Aug 2013, 12:51
4
KUDOS
19
This post was
BOOKMARKED
00:00

Difficulty:

5% (low)

Question Stats:

76% (01:08) correct 24% (01:14) wrong based on 576 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

--------------------
[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 ^_^

Kudos [?]: 120 [4], given: 137

Director
Joined: 14 Dec 2012
Posts: 832

Kudos [?]: 1630 [3], given: 197

Location: India
Concentration: General Management, Operations
GMAT 1: 700 Q50 V34
GPA: 3.6
Re: Is |xy| > x^2*y^2 ? [#permalink]

### Show Tags

17 Aug 2013, 13:01
3
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
$$(xy)^2 > (xy)^4$$
$$(xy)^2((xy)^2-1)<0$$
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...

learn AWA writing techniques while watching video : http://www.gmatprepnow.com/module/gmat-analytical-writing-assessment

Last edited by blueseas on 17 Aug 2013, 15:16, edited 1 time in total.

Kudos [?]: 1630 [3], given: 197

Manager
Joined: 04 Apr 2013
Posts: 149

Kudos [?]: 58 [0], given: 36

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
$$(xy)^2 > (xy)^4$$
$$(xy)^2((xy)^2-1)<0$$
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
_________________

MGMAT1 - 540 ( Trying to improve )

Kudos [?]: 58 [0], given: 36

Director
Joined: 14 Dec 2012
Posts: 832

Kudos [?]: 1630 [1], given: 197

Location: India
Concentration: General Management, Operations
GMAT 1: 700 Q50 V34
GPA: 3.6
Re: Is |xy| > x^2*y^2 ? [#permalink]

### Show Tags

17 Aug 2013, 15:17
1
KUDOS

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...

learn AWA writing techniques while watching video : http://www.gmatprepnow.com/module/gmat-analytical-writing-assessment

Kudos [?]: 1630 [1], given: 197

Director
Joined: 25 Apr 2012
Posts: 722

Kudos [?]: 865 [0], given: 724

Location: India
GPA: 3.21

### Show Tags

24 Jul 2014, 20:33
Q. $$Is |xy|>x^{2}y^{2}$$

1.$$0<x^{2}<1/4$$
2. $$0<y^{2}<1/9$$

[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.”

Kudos [?]: 865 [0], given: 724

Manager
Joined: 21 Jul 2014
Posts: 127

Kudos [?]: 164 [7], given: 12

### Show Tags

24 Jul 2014, 20:49
7
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.

Kudos [?]: 164 [7], given: 12

Intern
Joined: 03 Jul 2013
Posts: 33

Kudos [?]: 24 [0], given: 0

### 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

Kudos [?]: 24 [0], given: 0

Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 7736

Kudos [?]: 17782 [9], given: 235

Location: Pune, India

### Show Tags

24 Jul 2014, 22:39
9
KUDOS
Expert's post
11
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.

_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Get started with Veritas Prep GMAT On Demand for \$199

Veritas Prep Reviews

Kudos [?]: 17782 [9], given: 235

Math Expert
Joined: 02 Sep 2009
Posts: 42249

Kudos [?]: 132631 [1], given: 12326

Re: Is |xy| > x^2*y^2 ? [#permalink]

### Show Tags

25 Jul 2014, 00:28
1
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.
_________________

Kudos [?]: 132631 [1], given: 12326

Manager
Joined: 11 Sep 2013
Posts: 149

Kudos [?]: 149 [1], given: 161

Concentration: Finance, Finance
Re: GMAT prep question pack 1 [#permalink]

### Show Tags

18 Aug 2014, 23:26
1
KUDOS
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

Kudos [?]: 149 [1], given: 161

Non-Human User
Joined: 09 Sep 2013
Posts: 15704

Kudos [?]: 282 [0], given: 0

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.
_________________

Kudos [?]: 282 [0], given: 0

Intern
Joined: 15 Dec 2015
Posts: 45

Kudos [?]: 7 [0], given: 32

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?

Kudos [?]: 7 [0], given: 32

Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 4318

Kudos [?]: 3037 [0], given: 0

GPA: 3.82
Re: Is |xy| > x^2*y^2 ? [#permalink]

### Show Tags

15 Dec 2015, 22:15
Expert's post
1
This post was
BOOKMARKED
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.
“Receive 5 Math Questions & Solutions Daily”
Unlimited Access to over 120 free video lessons - try it yourself

Kudos [?]: 3037 [0], given: 0

Non-Human User
Joined: 09 Sep 2013
Posts: 15704

Kudos [?]: 282 [0], given: 0

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.
_________________

Kudos [?]: 282 [0], given: 0

Re: Is |xy| > x^2*y^2 ?   [#permalink] 14 Feb 2017, 11:03
Display posts from previous: Sort by

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

 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®.