BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

MGMAT Test question wrong?

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
User avatar
Master | Next Rank: 500 Posts
Posts: 183
Joined: Wed Sep 21, 2011 7:06 am
Location: Washington, DC
Thanked: 6 times
Followed by:2 members
GMAT Score:500

MGMAT Test question wrong?

by Rastis » Mon Sep 15, 2014 10:54 am
If x and y are positive and x2y2 = 18 - 3xy, then x2 =

A) (18 - 3y)/y^3

B) 18/y^2

C) 18/(y^2 + 3y)

D) 9/y^2

E) 36/y^2

They say the answer is D but I believe the answer is B. If you plug in 3 for "y" and solve you get x=2 (because x,y are positive). If you plug 3 into B you get an answer of 2. Am I wrong?
Top
Source: — Problem Solving |
Junior | Next Rank: 30 Posts
Posts: 24
Joined: Sun Apr 13, 2014 6:13 am

by gmatcracker0123 » Mon Sep 15, 2014 11:59 am
Rastis wrote:If x and y are positive and x2y2 = 18 - 3xy, then x2 =

A) (18 - 3y)/y^3

B) 18/y^2

C) 18/(y^2 + 3y)

D) 9/y^2

E) 36/y^2

They say the answer is D but I believe the answer is B. If you plug in 3 for "y" and solve you get x=2 (because x,y are positive). If you plug 3 into B you get an answer of 2. Am I wrong?
Is the question x^2 * y^2 = 18 - 3xy then x^2 = ?
Top
User avatar
Master | Next Rank: 500 Posts
Posts: 183
Joined: Wed Sep 21, 2011 7:06 am
Location: Washington, DC
Thanked: 6 times
Followed by:2 members
GMAT Score:500

by Rastis » Mon Sep 15, 2014 12:06 pm
Yes. Sorry for the confusion.
Top
Junior | Next Rank: 30 Posts
Posts: 24
Joined: Sun Apr 13, 2014 6:13 am

by gmatcracker0123 » Mon Sep 15, 2014 12:33 pm
Following your approach
When y=3 --> x=2

As you have been asked the value of x^2, the answers should after plugging in y=3 should yield 4 and not 2.
Ans E satisfies this value as 36/(y^2) = 36/(3^2) = 36/9 = 4 = 2^2 = x^2
Top

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 16207
Joined: Mon Dec 08, 2008 6:26 pm
Location: Vancouver, BC
Thanked: 5254 times
Followed by:1268 members
GMAT Score:770

by Brent@GMATPrepNow » Mon Sep 15, 2014 12:36 pm
Rastis wrote:If x and y are positive and x²y² = 18 - 3xy, then x² =

A) (18 - 3y)/y³

B) 18/y²

C) 18/(y² + 3y)

D) 9/y²

E) 36/y²
x²y² = 18 - 3xy = (xy)² = 18 - 3xy
To make it easier to solve this equation, let k = xy
We get: k² = 18 - 3k
Rewrite as: k² + 3k - 18 = 0
Factor: (k + 6)(k - 3)
So, EITHER k = -6 OR k = 3
This means that EITHER xy = -6 OR xy = 3

case a: xy = -6
Since x and y are both POSITIVE, xy cannot equal -6.
So, we can rule out case a.

case b: xy = 3
Since x and y are both POSITIVE, it's possible for xy to equal 3.

If xy = 3, then ( xy)² = 3²
Simplify to get: x²y² = 9
Divide both sides by y² to get: x² = [spoiler]9/y²[/spoiler]

Answer: D

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
Image
Top

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 16207
Joined: Mon Dec 08, 2008 6:26 pm
Location: Vancouver, BC
Thanked: 5254 times
Followed by:1268 members
GMAT Score:770

by Brent@GMATPrepNow » Mon Sep 15, 2014 12:42 pm
Rastis wrote:If x and y are positive and x²y² = 18 - 3xy, then x² =

A) (18 - 3y)/y³

B) 18/y²

C) 18/(y² + 3y)

D) 9/y²

E) 36/y²

They say the answer is D but I believe the answer is B. If you plug in 3 for "y" and solve you get x=2 (because x,y are positive). If you plug 3 into B you get an answer of 2. Am I wrong?
The statement in green is not true.
If we let y = 3, we get: x²(3)² = 18 - 3x(3)
Simplify: 9x² = 18 - 9x
Rearrange: 9x² + 9x - 18 = 0
Divide both sides by 9 to get: x² + x - 2 = 0
Factor to get: (x + 2)(x - 1) = 0
So, x = -2 or x = 1
Since x is POSITIVE, it must be the case that x = 1 (when y = 3)

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
Image
Top

GMAT/MBA Expert

User avatar
Elite Legendary Member
Posts: 10392
Joined: Sun Jun 23, 2013 6:38 pm
Location: Palo Alto, CA
Thanked: 2867 times
Followed by:511 members
GMAT Score:800

by [email protected] » Mon Sep 15, 2014 1:06 pm
Hi Rastis,

This question has a "quirky" design element to it - it takes a bit longer than normal to solve AND you might have to TEST VALUES TWICE to get to the correct answer.

If you TEST Y = 3, then X = 1 (as Brent pointed out). Then, the answer to the question is also 1 (1² = 1). Plugging Y = 3 into the answer choices gets us 2 answers that match:

C = 18/(3² + 9) = 18/18 = 1
D = 9/3² = 9/9 = 1

None of the other answers matches, so we're down to 2 choices. At this point, you can either guess one of the 2 or go back and TEST a new value.

If we use Y = 2 in the original equation, then we have
4X² = 18 - 6X
4X² +6X - 18 = 0
2X² +3X - 9 = 0

Factoring this down might seem a little strange, but it DOES lead to a solution...
(X + 3)(2X - 3) = 0
X = -3 or +3/2

Since we're told that X and Y are both POSITIVE, X = 3/2

So now we plug Y = 2 into the answers and we're looking for (3/2)² = 9/4

Answer C: 18/10 = 9/5
Answer D: 9/4

Final Answer: D

GMAT assassins aren't born, they're made,
Rich
Contact Rich at [email protected]
Image
Top
Legendary Member
Posts: 510
Joined: Thu Aug 07, 2014 2:24 am
Thanked: 3 times
Followed by:5 members

by j_shreyans » Tue Sep 16, 2014 10:07 pm
Hi Guys ,

We can also solve this question through middle term :

x^2y^2=18-3xy

x^2y^2+3xy-18=0

x^2y^2+6xy-3xy-18=0
xy(xy+6)-3(xy+6)=0

(xy-3)(xy+6)=0

xy=3 and xy=-6

as given x and y are positive so we will take xy=3


now for xy=3

x must be 1 or 3

put both the value in options you will get the answer .

option D satisfy
Top
Post new topic Post Reply
• Page 1 of 1