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

 It is currently 24 May 2013, 17:49

# 8x y^3 + 8x^3 y = 2x^2y^2 * 8 , What is xy? (1) y > x (2)

Author Message
TAGS:
Senior Manager
Joined: 31 Oct 2010
Posts: 493
Location: India
Concentration: Entrepreneurship, Strategy
GMAT 1: 710 Q48 V40
WE: Project Management (Manufacturing)
Followers: 10

Kudos [?]: 31 [0], given: 67

8x y^3 + 8x^3 y = 2x^2y^2 * 8 , What is xy? (1) y > x (2) [#permalink]  31 Mar 2011, 12:00
00:00

Question Stats:

33% (03:11) correct 66% (01:38) wrong based on 0 sessions
8x y^3 + 8x^3 y= 2x^2y^2 * 8, What is xy?

(1) y > x

(2) x < 0

How I approached it:

We can simplify the given equation as:

8xy (x^2+y^2)= 2xy. xy. 8
=> x^2+y^2=2xy
=> x^2+y^2-2xy=0
=>(x-y)^2= 0
=> (x-y)=0
=> x=y

You see I'm getting x=y, which is in direct contradiction with Statement (1), something that cannot happen on the GMAT. Can someone please tell me where am I going wrong?
[Reveal] Spoiler: OA

_________________

My GMAT debrief: from-620-to-710-my-gmat-journey-114437.html

 Kaplan GMAT Prep Discount Codes Knewton GMAT Discount Codes Manhattan GMAT Discount Codes
Math Forum Moderator
Joined: 20 Dec 2010
Posts: 2100
Followers: 108

Kudos [?]: 655 [2] , given: 376

Re: Inequalities DS: Help sought [#permalink]  31 Mar 2011, 12:29
2
KUDOS
gmatpapa wrote:
8x y^3 + 8x^3 y= 2x^2y^2 * 8, What is xy?

(1) y > x

(2) x < 0

How I approached it:

We can simplify the given equation as:

8xy (x^2+y^2)= 2xy. xy. 8
=> x^2+y^2=2xy
Never divide the variables if you don't know their value or sign
You have divided xy on both sides; RHS and LHS, which is illegal. What if either x or y is 0, then you would be dividing the polynomial with 0 and 0 in denominator is unacceptable. It results in undefined value.

=> x^2+y^2-2xy=0
=>(x-y)^2= 0
=> (x-y)=0
=> x=y

You see I'm getting x=y, which is in direct contradiction with Statement (1), something that cannot happen on the GMAT. Can someone please tell me where am I going wrong?

Sol:
I am going to follow your main idea i.e. to reduce the expression to its simplest form:

8xy^3 + 8x^3y= 2x^2y^2*8
8xy(y^2 + x^2)= 2*x^2y^2*8

Dividing by 8 on both sides; we can do this because 8 is a constant and we know its value
xy(y^2 + x^2)= 2*x^2y^2

Subtract 2*x^2y^2 from both sides
xy(y^2 + x^2) - 2*x^2y^2 = 0

Taking xy common
xy(y^2 + x^2 - 2xy) = 0
xy(y-x)^2 = 0

The expression above means either at least one of x and y is 0 OR y-x=0 i.e. x=y

1. y>x
It means x \ne y
That leaves us with only one case; At least one of x and y is 0
And xy=0
Sufficient.

2. x<0
It means x can be any negative number.
Now, {x,y} can be {-1,-1} or {-100,-100} both incurring different results when multiplied.
Insufficient.

Ans: "A"
_________________
Senior Manager
Joined: 31 Oct 2010
Posts: 493
Location: India
Concentration: Entrepreneurship, Strategy
GMAT 1: 710 Q48 V40
WE: Project Management (Manufacturing)
Followers: 10

Kudos [?]: 31 [0], given: 67

Re: Inequalities DS: Help sought [#permalink]  31 Mar 2011, 12:41
fluke wrote:
Never divide the variables if you don't know their value or sign
You have divided xy on both sides; RHS and LHS, which is illegal. What if either x or y is 0, then you would be dividing the polynomial with 0 and 0 in denominator is unacceptable. It results in undefined value.

Oh.. I always thought this restriction applies to only inequalities. The OE is the exact same as yours. I understood it but was wondering why cant we divide the equation with xy so we get (x-y)^2=0. Thanks for the explanation, fluke.
_________________

My GMAT debrief: from-620-to-710-my-gmat-journey-114437.html

SVP
Joined: 16 Nov 2010
Posts: 1721
Location: United States (IN)
Concentration: Strategy, Technology
Followers: 26

Kudos [?]: 228 [0], given: 34

Re: Inequalities DS: Help sought [#permalink]  31 Mar 2011, 19:26
The expression says :

8xy^3 + 8x^3y - 2x^2y^2*8 = 0

xy^3 + x^3y - x^2y^2 = 0

xy(y^2 + x^2 - 2xy) = 0

xy (x - y)^2 = 0

So either xy = 0 or (x-y)^2 = 0

(1) y > x

=> (x-y)^2 != 0, so xy = 0

(2) x < 0, but no information about y, so insufficient as y = 0, or y = x is possible too.

_________________

Formula of Life -> Achievement/Potential = k * Happiness (where k is a constant)

Find out what's new at GMAT Club - latest features and updates

Director
Joined: 01 Feb 2011
Posts: 791
Followers: 11

Kudos [?]: 63 [0], given: 42

Re: Inequalities DS: Help sought [#permalink]  03 Apr 2011, 07:53
solving the given expression

we have
8xy(x2+y2-2xy) = 0
=> xy(x-y)^2 =0
=> either xy =0 or x=y

1. Sufficient
y>x =>xy=0

2. Not sufficient
x<0 ,no info on y. so xy could vary depending on the selected combination

Re: Inequalities DS: Help sought   [#permalink] 03 Apr 2011, 07:53
Similar topics Replies Last post
Similar
Topics:
What is {8x^3/4*y^2}^-1/3 4 30 Aug 2006, 01:33
8xy^3 + 8x^3y = (2 * x^2 * y^2)/2^-3 What is xy? (1) y > 14 08 Oct 2007, 00:37
xy not equal 0. is xy=70? 1. x>y 2. X^2 = y^2 Can someone 3 30 Dec 2007, 22:11
2 8xy^3 + 8x^3y = 2x^2*y^2 / 2^(-3), What is xy? 5 23 Feb 2012, 20:27
If 8xy^3 + 8x^3*y=2x^2*y^2/ 2^-3,what is the value of x? 3 24 Dec 2012, 06:18
Display posts from previous: Sort by