[Math Revolution GMAT math practice question]
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
If x and y are integers such that (xy)^2 + x^2 – 2xy – 2
This topic has expert replies
- Max@Math Revolution
- Elite Legendary Member
- Posts: 3991
- Joined: Fri Jul 24, 2015 2:28 am
- Location: Las Vegas, USA
- Thanked: 19 times
- Followed by:37 members
Timer
00:00
Your Answer
A
B
C
D
E
Global Stats
Math Revolution
The World's Most "Complete" GMAT Math Course!
Score an excellent Q49-51 just like 70% of our students.
[Free] Full on-demand course (7 days) - 100 hours of video lessons, 490 lesson topics, and 2,000 questions.
[Course] Starting $79 for on-demand and $60 for tutoring per hour and $390 only for Live Online.
Email to : [email protected]
- GMATGuruNY
- GMAT Instructor
- Posts: 15539
- Joined: Tue May 25, 2010 12:04 pm
- Location: New York, NY
- Thanked: 13060 times
- Followed by:1906 members
- GMAT Score:790
We can PLUG IN THE ANSWERS, which represent the value of y.Max@Math Revolution wrote:[Math Revolution GMAT math practice question]
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
B: y=-1
Substituting y=-1 into (xy)² + x² - 2xy - 2x + 2 = 0, we get:
x² + x² + 2x - 2x + 2 = 0
2x² + 2 = 0
x² + 1 = 0
x² = -1
Since the square of a value cannot be negative, eliminate B.
D: y=1
Substituting y=1 into (xy)² + x² - 2xy - 2x + 2 = 0, we get:
x² + x² - 2x - 2x + 2 = 0
2x² - 4x + 2 = 0
x² - 2x + 1 = 0
(x-1)² = 0
x = 1
Success!
The correct answer is D.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
GMAT/MBA Expert
- Jeff@TargetTestPrep
- GMAT Instructor
- Posts: 1462
- Joined: Thu Apr 09, 2015 9:34 am
- Location: New York, NY
- Thanked: 39 times
- Followed by:22 members
(xy)^2 + x^2 - 2xy - 2x + 2 = 0Max@Math Revolution wrote:[Math Revolution GMAT math practice question]
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
(xy)^2 - 2xy + 1 + x^2 - 2x + 1 = 0
(xy - 1)^2 + (x - 1)^2 = 0
If the sum of two squares is 0, each square must be 0 also.
(xy - 1)^2 = 0
xy - 1 = 0
xy = 1
and
(x - 1)^2 = 0
x - 1 = 0
x = 1
Since x = 1 and xy = 1, y must be 1 also.
Answer: D
Jeffrey Miller
Head of GMAT Instruction
[email protected]
See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews
- Max@Math Revolution
- Elite Legendary Member
- Posts: 3991
- Joined: Fri Jul 24, 2015 2:28 am
- Location: Las Vegas, USA
- Thanked: 19 times
- Followed by:37 members
=>
(xy)^2 + x^2 - 2xy - 2x + 2 = 0
=> (xy)^2 - 2xy + 1 + x^2 - 2x + 1 = 0
=> (xy - 1)^2 + (x - 1)2 = 0
=> xy = 1 and x = 1.
Thus , x = 1 and y = 1.
Therefore, the answer is D.
Answer: D
(xy)^2 + x^2 - 2xy - 2x + 2 = 0
=> (xy)^2 - 2xy + 1 + x^2 - 2x + 1 = 0
=> (xy - 1)^2 + (x - 1)2 = 0
=> xy = 1 and x = 1.
Thus , x = 1 and y = 1.
Therefore, the answer is D.
Answer: D
Math Revolution
The World's Most "Complete" GMAT Math Course!
Score an excellent Q49-51 just like 70% of our students.
[Free] Full on-demand course (7 days) - 100 hours of video lessons, 490 lesson topics, and 2,000 questions.
[Course] Starting $79 for on-demand and $60 for tutoring per hour and $390 only for Live Online.
Email to : [email protected]