February 17, 2019 February 17, 2019 07:00 AM PST 09:00 AM PST Attend this Free Algebra Webinar and learn how to master Inequalities and Absolute Value problems on GMAT. February 18, 2019 February 18, 2019 10:00 PM PST 11:00 PM PST We don’t care what your relationship status this year  we love you just the way you are. AND we want you to crush the GMAT!
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 x − 2y equal?
[#permalink]
Show Tags
28 Feb 2012, 20:12
Question Stats:
73% (02:29) correct 27% (02:55) wrong based on 467 sessions
HideShow timer Statistics
If x + y = 2 and x^2  xy  10  2y^2 = 0, what does x − 2y equal? 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: 52906

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




Current Student
Joined: 23 May 2013
Posts: 186
Location: United States
Concentration: Technology, Healthcare
GPA: 3.5

Re: If x + y = 2 and x^2  xy  10  2y^2 = 0, what does x − 2y equal?
[#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 x − 2y equal?
[#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: 188

Re: If x + y = 2 and x^2  xy  10  2y^2 = 0, what does x − 2y equal?
[#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 x − 2y equal?
[#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: 52906

Re: If x + y = 2 and x^2  xy  10  2y^2 = 0, what does x − 2y equal?
[#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 x − 2y equal?
[#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: 275

Re: If x + y = 2 and x^2  xy  10  2y^2 = 0, what does x − 2y equal?
[#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: 1821
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 x − 2y equal?
[#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: 2587
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 x − 2y equal?
[#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.



Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 6949
GPA: 3.82

Re: If x + y = 2 and x^2  xy  10  2y^2 = 0, what does x − 2y equal?
[#permalink]
Show Tags
14 Dec 2015, 04:31
Forget conventional ways of solving math questions. In PS, IVY approach is the easiest and quickest way to find the answer. If x + y = 2 and x^2  xy  10  2y^2 = 0, what does x − 2y equal? A. 0 B. 1 C. 2 D. 5 E. 10 Since x + y = 2 we have y=2x. So 0= x^2  xy  10  2y^2 = x^2  x(2x)  10  2(2x)^2 = x^2 2x+x^2 108+8x2x^2 = x=6x18. > x=3 > y= 1 >x2y=5 The answer is (D).
_________________
MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The oneandonly World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only $149 for 3 month Online Course" "Free Resources30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons  try it yourself"



Intern
Joined: 30 May 2014
Posts: 15
WE: Information Technology (Consulting)

Re: If x + y = 2 and x^2  xy  10  2y^2 = 0, what does x − 2y equal?
[#permalink]
Show Tags
14 Dec 2015, 04:59
Bunuel wrote: If x + y = 2 and x^2  xy  10  2y^2 = 0, what does x − 2y equal?
A. 0 B. 1 C. 2 D. 5 E. 10 x^2  xy  2y^2 = 10 by seeing the x^2 and 2^y attributes, (by trail and error method) (x2y) (x+y) = 10 Given x+y = 2 x2y = 10/2 = 5 (Answer D)



Manager
Joined: 18 Nov 2013
Posts: 78
Concentration: General Management, Technology

Re: If x + y = 2 and x^2  xy  10  2y^2 = 0, what does x − 2y equal?
[#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: 08 Jan 2015
Posts: 6
Location: India
Concentration: Strategy, Operations
GMAT 1: 650 Q40 V40 GMAT 2: 650 Q48 V41 GMAT 3: 720 Q48 V41
GPA: 2.8
WE: Analyst (Internet and New Media)

Re: If x + y = 2 and x^2  xy  10  2y^2 = 0, what does x − 2y equal?
[#permalink]
Show Tags
18 Feb 2017, 04:48
Hi.. i solved the question by substitution method , but i see the equation can be factorised too as per 2 nd soln. How has it been factorised?



Intern
Joined: 12 Sep 2015
Posts: 3

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






