November 17, 2018 November 17, 2018 07:00 AM PST 09:00 AM PST Nov. 17, 7 AM PST. Aiming to score 760+? Attend this FREE session to learn how to Define your GMAT Strategy, Create your Study Plan and Master the Core Skills to excel on the GMAT. November 17, 2018 November 17, 2018 09:00 AM PST 11:00 AM PST Join the Quiz Saturday November 17th, 9 AM PST. The Quiz will last approximately 2 hours. Make sure you are on time or you will be at a disadvantage.
Author 
Message 
TAGS:

Hide Tags

Intern
Joined: 25 Jan 2012
Posts: 4

If x+y=2 and x^2  xy  10  2y^2 = 0, what does x2y =?
[#permalink]
Show Tags
28 Feb 2012, 20:12
Question Stats:
72% (02:32) correct 28% (02:57) wrong based on 436 sessions
HideShow timer Statistics
If x+y=2 and x^2  xy  10  2y^2 = 0, what does x2y =? A. 0 B. 1 C. 2 D. 5 E. 10
Official Answer and Stats are available only to registered users. Register/ Login.




Math Expert
Joined: 02 Sep 2009
Posts: 50617

Re: If x+y=2 and x^2  xy  10  2y^2 = 0, what does x2y =?
[#permalink]
Show Tags
28 Feb 2012, 22:12




Current Student
Joined: 23 May 2013
Posts: 188
Location: United States
Concentration: Technology, Healthcare
GPA: 3.5

Re: If x+y=2 and x^2  xy  10  2y^2 = 0, what does x2y =?
[#permalink]
Show Tags
28 May 2014, 06:21
vintage83 wrote: If x+y=2 and x^2  xy  10  2y^2 = 0, what does x2y =?
A. 0 B. 1 C. 2 D. 5 E. 10 This problem can still be easily solved without utilizing a "trick" in the algebra; you have two equations, just solve for x & y. \(x + y = 2\) \(y = x 2\) \(x^2  xy  10  2y^2 = 0\) \(x^2  x(2x)  10  2(x^2  4x +4)\) \(x^2  2x +x^2  10  2x^2 + 8x 8\) Here, the quadratic conveniently cancels out, so we're left with a linear equation. \(6x  18 = 0,\) \(x = 3.\) Using x = 3 and our first equation, we have that y = 1, and thus that x  2y = 3  2(1) = 3+2 = 5. Answer: D.




Intern
Joined: 24 Feb 2012
Posts: 31

Re: If x+y=2 and x^2  xy  10  2y^2 = 0, what does x2y =?
[#permalink]
Show Tags
28 Feb 2012, 22:46
Very tricky....I confess...I knew there was a simpler route.....but I just did not see it.



Current Student
Joined: 21 Aug 2010
Posts: 190

Re: If x+y=2 and x^2  xy  10  2y^2 = 0, what does x2y =?
[#permalink]
Show Tags
29 Feb 2012, 02:22
Square the first equation and subtract from the second and there you are.
You would be able to factor out and find the values of x and y. x = 3 and y = 1
x  2y => 3  2(1) = 5
BR Mandeep



Intern
Joined: 25 Jan 2012
Posts: 4

Re: If x+y=2 and x^2  xy  10  2y^2 = 0, what does x2y =?
[#permalink]
Show Tags
29 Feb 2012, 06:33
Thank you very much. I get it now! I think I got confused at the last step and was stuck for a while.



Math Expert
Joined: 02 Sep 2009
Posts: 50617

Re: If x+y=2 and x^2  xy  10  2y^2 = 0, what does x2y =?
[#permalink]
Show Tags
03 Jul 2013, 00:24



Verbal Forum Moderator
Joined: 10 Oct 2012
Posts: 611

Re: If x+y=2 and x^2  xy  10  2y^2 = 0, what does x2y =?
[#permalink]
Show Tags
03 Jul 2013, 01:54
vintage83 wrote: If x+y=2 and x^2  xy  10  2y^2 = 0, what does x2y =?
A. 0 B. 1 C. 2 D. 5 E. 10 Given that \(x^2  xy  10  2y^2 = 0 \to x^2+4y^24xy10xy2y^2=4y^24xy\) [By adding \(4y^2\) and \(4xy\) on both sides]\(\to\) \((x2y)^2 = 6y^23xy+10\) Or \((x2y)^2 = 3y(2yx)+10 \to (x2y)^2+3y(x2y) = 10\to (x2y)(x2y+3y) = 10 \to (x2y) = \frac{10}{x+y}\) = 5. D.
_________________
All that is equal and notDeep Dive Inequality
Hit and Trial for Integral Solutions



Senior Manager
Joined: 13 Jun 2013
Posts: 276

Re: If x+y=2 and x^2  xy  10  2y^2 = 0, what does x2y =?
[#permalink]
Show Tags
28 May 2014, 11:26
vintage83 wrote: If x+y=2 and x^2  xy  10  2y^2 = 0, what does x2y =?
A. 0 B. 1 C. 2 D. 5 E. 10 x+y=2 1); squaring both sides we have; (x+y)^2=4 2); Now, x^2=10+2y^2+xy; adding y^2 and 2xy on both sides we have; x^2+y^2+2xy = 10+ 3y^2+3xy; (x+y)^2= 10+ 3y^2+3xy; from 2) we have 4=10+ 3y^2+3xy; 6=3y(x+y); from 1) x+y=2 6=6y; y= 1; therefore x=3 from 1) thus x2y= 3(2)=5



SVP
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1826
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)

Re: If x+y=2 and x^2  xy  10  2y^2 = 0, what does x2y =?
[#permalink]
Show Tags
15 Jul 2014, 22:24
\(x^2  xy  10  2y^2 = 0\)
\(x^2  2xy + xy  2y^2 = 10\)
x(x2y) + y(x2y) = 10
(x+y)(x2y) = 10
\(x2y = \frac{10}{x+y} = \frac{10}{2} = 5\)
Answer = D



Board of Directors
Joined: 17 Jul 2014
Posts: 2645
Location: United States (IL)
Concentration: Finance, Economics
GPA: 3.92
WE: General Management (Transportation)

Re: If x+y=2 and x^2  xy  10  2y^2 = 0, what does x2y =?
[#permalink]
Show Tags
22 Nov 2015, 10:19
oh man..tricky one..I couldn't see the short way to solve it:
(x+y) = 2 and (x+y)^2 = 4 multiply the second equation by 2 and get: 2x^2 2xy204y^2 = 0 now add 2 equations 2x^2 2xy204y^2 = 0+ x^2 +2xy +y^2 = 4
we get: 3x^2 20  3y^2 = 4 or 3x^2  3y^2 = 24 divide by 3: x^2  y^2 = 8 rewrite the equation: (x+y)(xy) = 8 we have x+y = 2, that means xy = 4 x=4+y
4+y+y = 2 2y +4 = 2 y = 1
ok, now get to x: x1 = 2 => x=3
x2y = 3(2) = 3+2 = 5.



Manager
Joined: 18 Nov 2013
Posts: 79
Concentration: General Management, Technology

Re: If x+y=2 and x^2  xy  10  2y^2 = 0, what does x2y =?
[#permalink]
Show Tags
20 Mar 2016, 10:54
I went with squaring the eq 1 and using that in eq 2 eq 1 : \(x+y=2\) \((x+y)^2=4\) > or ( \(x^2 + 2xy + y^2 = 4\)) now, eq 2 : \(x^2  xy  2y^2 = 10\) \(x^2 + 2xy + y^2 2xy  y^2 xy 2y^2 = 10\) > adding and substracting (2xy + y^2) \((x+y)^2 3xy 3y^2 = 10\) \((x+y)^2 3y(x +y) = 10\) \(4 3y(2) = 10\) \(3y = 3\) > y = 1 \(y = 1\) , and \(x = 3\) (from x+y=2) \(x2y =5\) Answer = D
_________________
_______  Cheers
+1 kudos if you like



Intern
Joined: 12 Sep 2015
Posts: 3

If x+y=2 and x^2  xy  10  2y^2 = 0, what does x2y =?
[#permalink]
Show Tags
19 Feb 2017, 01:21
vintage83 wrote: If x+y=2 and x^2  xy  10  2y^2 = 0, what does x2y =?
A. 0 B. 1 C. 2 D. 5 E. 10 I just did the small logic that is x^2(1)xy2y^2=10 If I do factor then it will be like (x2y)(x+y)=10 (x2y)2=10 .......................As given (x+y)=2 (x2y)=5 Ans is D Please correct if i am wrong.



Intern
Joined: 14 Jun 2018
Posts: 47
Location: India
Concentration: International Business, Marketing

Re: If x+y=2 and x^2  xy  10  2y^2 = 0, what does x2y =?
[#permalink]
Show Tags
05 Sep 2018, 23:17
eaze wrote: vintage83 wrote: If x+y=2 and x^2  xy  10  2y^2 = 0, what does x2y =?
A. 0 B. 1 C. 2 D. 5 E. 10 This problem can still be easily solved without utilizing a "trick" in the algebra; you have two equations, just solve for x & y. \(x + y = 2\) \(y = x 2\) \(x^2  xy  10  2y^2 = 0\) \(x^2  x(2x)  10  2(x^2  4x +4)\) \(x^2  2x +x^2  10  2x^2 + 8x 8\) Here, the quadratic conveniently cancels out, so we're left with a linear equation. \(6x  18 = 0,\) \(x = 3.\) Using x = 3 and our first equation, we have that y = 1, and thus that x  2y = 3  2(1) = 3+2 = 5. Answer: D. Hello, In the second step, shouldn't y=(x+2) instead of y=x2 ? please correct me




Re: If x+y=2 and x^2  xy  10  2y^2 = 0, what does x2y =? &nbs
[#permalink]
05 Sep 2018, 23:17






