Forum Home > GMAT > Quantitative > Problem Solving (PS)
Events & Promotions
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
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Jul 2710:00 AM PDT
-11:00 AM PDT
Are you struggling with the GMAT verbal section? Do tricky questions and lengthy passages overwhelm you? Don't worry—I've got you covered! In this video, I'll provide a detailed, actionable plan to help you significantly boost your verbal score.
Jul 2711:00 AM IST
-01:00 PM IST
Attend this session to learn how to Deconstruct arguments, Pre-Think Author’s Assumptions, and apply Negation Test.
Jul 2508:00 AM EDT
-11:59 PM EDT
More and more TTP students are earning impressive scores on the GMAT. Now is the perfect time to join the many GMAT students who made the switch to TTP and surpassed their wildest expectations on test day.- Jul 28
10:00 AM PDT
-11:00 AM PDT
We will learn how to guess an answer choice better on the GMAT. If you are running out of time and want to guess on a few questions, these effective techniques will help you in making a smart guess. - Jul 28
11:00 AM IST
-01:00 PM IST
Attend this free GMAT Algebra Webinar and learn how to master the most challenging Inequalities and Absolute Value problems with ease. - Jul 31
05:55 AM PDT
-12:30 PM PDT
MBA Application Walkthrough and Essay Review. You will have a chance to hear from experts covering the Top 15 MBA programs, covering details of the application and essays. 
Jul 3110:00 AM EDT
-11:59 PM PDT
Save 20% on Target Test Prep and Score in the 100th Percentile in GMAT Verbal! Our course uses techniques such as topical study and spaced repetition to maximize knowledge retention and make studying simple and fun.
If x and y are integers such that (xy)^2 + x^2 2xy 2x + 2 = 0
[#permalink]
01 Nov 2022, 02:05
01 Nov 2022, 02:05
13
Bookmarks
Expert Reply
Show timer
00:00
A
B
C
D
E
Difficulty:
55%
(hard)
Question Stats:
66% (02:31) correct
34%
(02:30)
wrong
based on 177
sessions
If \(x\) and \(y\) are integers such that \((xy)^2 + x^2 – 2xy – 2x + 2 = 0\), what is the value of \(y\)?
A. -2
B. -1
C. 0
D. 1
E. 2
A. -2
B. -1
C. 0
D. 1
E. 2
Quant Chat Moderator
Joined: 22 Dec 2016
Posts: 3125
Given Kudos: 1859
Location: India
Concentration: Strategy, Leadership
If x and y are integers such that (xy)^2 + x^2 2xy 2x + 2 = 0
[#permalink]
Updated on: 01 Nov 2022, 09:45
Updated on: 01 Nov 2022, 09:45
4
Kudos
2
Bookmarks
We can re-write the equation \((xy)^2 + x^2 – 2xy – 2x + 2 = 0\) as
\((xy - 1)^2 + (x-1)^2 = 0\)
\((xy - 1)^2\) is non negative and \((x-1)^2\) is non negative, the sum can be zero only if individual terms is 0.
Thus x - 1 = 0
x = 1
xy - 1 = 0
y - 1 = 0
Therefore y = 1
IMO D
\((xy - 1)^2 + (x-1)^2 = 0\)
\((xy - 1)^2\) is non negative and \((x-1)^2\) is non negative, the sum can be zero only if individual terms is 0.
Thus x - 1 = 0
x = 1
xy - 1 = 0
y - 1 = 0
Therefore y = 1
IMO D
Originally posted by gmatophobia on 01 Nov 2022, 02:29.
Last edited by gmatophobia on 01 Nov 2022, 09:45, edited 1 time in total.
Last edited by gmatophobia on 01 Nov 2022, 09:45, edited 1 time in total.
Corrected the solution
General Discussion
Re: If x and y are integers such that (xy)^2 + x^2 2xy 2x + 2 = 0
[#permalink]
01 Nov 2022, 09:15
01 Nov 2022, 09:15
2
Kudos
gmatophobia wrote:
We can re-write the equation \((xy)^2 + x^2 – 2xy – 2x + 2 = 0\) as
\((xy - x)^2 = 2x - 2\)
\((xy - x)^2 = 2(x - 2)\)
As the left hand side of the equation is a square, the right hand side of the equation must be greater than or equal to 0
So \(2(x-2) \geq{0}\)
Therefore \( x\geq{0}\)
Now we know that for any value of \( x\geq{0}\), the equation should satisfy.
Let's take x = 2
\((2y - 2)^2 = 2(2 - 2)\)
\((2y - 2)^2 = 0\)
Therefore y = 1
IMO D
\((xy - x)^2 = 2x - 2\)
\((xy - x)^2 = 2(x - 2)\)
As the left hand side of the equation is a square, the right hand side of the equation must be greater than or equal to 0
So \(2(x-2) \geq{0}\)
Therefore \( x\geq{0}\)
Now we know that for any value of \( x\geq{0}\), the equation should satisfy.
Let's take x = 2
\((2y - 2)^2 = 2(2 - 2)\)
\((2y - 2)^2 = 0\)
Therefore y = 1
IMO D
\((xy - x)^2 = 2x - 2\)
I'm afraid, I don't understand.
\((xy - x)^2 = x^2y^2 + x^2 - 2x^2y\)
How can we re-write \(x^2y^2 + x^2 - 2xy\) as \((xy - x)^2\)
