If x+y=2 and x^2 - xy - 10 - 2y^2 = 0, what does x-2y =? : GMAT Problem Solving (PS)
Check GMAT Club Decision Tracker for the Latest School Decision Releases https://gmatclub.com/AppTrack

 It is currently 22 Feb 2017, 14:14

### 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

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# If x+y=2 and x^2 - xy - 10 - 2y^2 = 0, what does x-2y =?

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

### Hide Tags

Intern
Joined: 25 Jan 2012
Posts: 4
Followers: 0

Kudos [?]: 15 [4] , given: 0

If x+y=2 and x^2 - xy - 10 - 2y^2 = 0, what does x-2y =? [#permalink]

### Show Tags

28 Feb 2012, 20:12
4
KUDOS
13
This post was
BOOKMARKED
00:00

Difficulty:

45% (medium)

Question Stats:

74% (03:12) correct 26% (02:40) wrong based on 330 sessions

### HideShow timer Statistics

If x+y=2 and x^2 - xy - 10 - 2y^2 = 0, what does x-2y =?

A. 0
B. 1
C. 2
D. 5
E. 10
[Reveal] Spoiler: OA
Math Expert
Joined: 02 Sep 2009
Posts: 37083
Followers: 7243

Kudos [?]: 96332 [6] , given: 10737

Re: If x+y=2 and x^2 - xy - 10 - 2y^2 = 0, what does x-2y =? [#permalink]

### Show Tags

28 Feb 2012, 22:12
6
KUDOS
Expert's post
5
This post was
BOOKMARKED
vintage83 wrote:
If x+y=2 and x^2 - xy - 10 - 2y^2 = 0, what does x-2y =?

A. 0
B. 1
C. 2
D. 5
E. 10

Hi,

Thanks much.

Welcome to GMAT Club. Below is a solution to your question.

Given: $$x^2-xy-10-2y^2=0$$;

Rearrange $$x^2-y^2-y^2-xy-10=0$$;

Apply $$a^2-b^2=(a-b)(a+b)$$: $$(x-y)(x+y)-y^2-xy-10=0$$ --> $$(x-y)(x+y)-y(y+x)-10=0$$;

Factor out $$x+y$$: $$(x+y)(x-y-y)-10=0$$;

Since given that $$x+y=2$$, then we have that $$2(x-2y)-10=0$$ --> $$x-2y=5$$.

_________________
Intern
Joined: 24 Feb 2012
Posts: 33
Followers: 0

Kudos [?]: 15 [0], given: 18

Re: If x+y=2 and x^2 - xy - 10 - 2y^2 = 0, what does x-2y =? [#permalink]

### Show Tags

28 Feb 2012, 22:46
1
This post was
BOOKMARKED
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: 210
Followers: 2

Kudos [?]: 17 [0], given: 28

Re: If x+y=2 and x^2 - xy - 10 - 2y^2 = 0, what does x-2y =? [#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
Followers: 0

Kudos [?]: 15 [0], given: 0

Re: If x+y=2 and x^2 - xy - 10 - 2y^2 = 0, what does x-2y =? [#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: 37083
Followers: 7243

Kudos [?]: 96332 [1] , given: 10737

Re: If x+y=2 and x^2 - xy - 10 - 2y^2 = 0, what does x-2y =? [#permalink]

### Show Tags

03 Jul 2013, 00:24
1
KUDOS
Expert's post
Bumping for review and further discussion*. Get a kudos point for an alternative solution!

*New project from GMAT Club!!! Check HERE

Theory on Algebra: algebra-101576.html

DS Algebra Questions to practice: search.php?search_id=tag&tag_id=29
PS Algebra Questions to practice: search.php?search_id=tag&tag_id=50

Special algebra set: new-algebra-set-149349.html

_________________
Verbal Forum Moderator
Joined: 10 Oct 2012
Posts: 630
Followers: 82

Kudos [?]: 1136 [1] , given: 136

Re: If x+y=2 and x^2 - xy - 10 - 2y^2 = 0, what does x-2y =? [#permalink]

### Show Tags

03 Jul 2013, 01:54
1
KUDOS
vintage83 wrote:
If x+y=2 and x^2 - xy - 10 - 2y^2 = 0, what does x-2y =?

A. 0
B. 1
C. 2
D. 5
E. 10

Given that $$x^2 - xy - 10 - 2y^2 = 0 \to x^2+4y^2-4xy-10-xy-2y^2=4y^2-4xy$$ [By adding $$4y^2$$ and $$4xy$$ on both sides]$$\to$$
$$(x-2y)^2 = 6y^2-3xy+10$$

Or $$(x-2y)^2 = 3y(2y-x)+10 \to (x-2y)^2+3y(x-2y) = 10\to (x-2y)(x-2y+3y) = 10 \to (x-2y) = \frac{10}{x+y}$$ = 5.
D.
_________________
Manager
Joined: 23 May 2013
Posts: 181
Location: United States
Concentration: Technology, Healthcare
GMAT 1: 760 Q49 V45
GPA: 3.5
Followers: 2

Kudos [?]: 73 [2] , given: 42

Re: If x+y=2 and x^2 - xy - 10 - 2y^2 = 0, what does x-2y =? [#permalink]

### Show Tags

28 May 2014, 06:21
2
KUDOS
2
This post was
BOOKMARKED
vintage83 wrote:
If x+y=2 and x^2 - xy - 10 - 2y^2 = 0, what does x-2y =?

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.

$$x + y = 2$$
$$y = x -2$$
$$x^2 - xy - 10 - 2y^2 = 0$$
$$x^2 - x(2-x) - 10 - 2(x^2 - 4x +4)$$
$$x^2 - 2x +x^2 - 10 - 2x^2 + 8x -8$$

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.

Senior Manager
Joined: 13 Jun 2013
Posts: 279
Followers: 13

Kudos [?]: 363 [0], given: 13

Re: If x+y=2 and x^2 - xy - 10 - 2y^2 = 0, what does x-2y =? [#permalink]

### Show Tags

28 May 2014, 11:26
vintage83 wrote:
If x+y=2 and x^2 - xy - 10 - 2y^2 = 0, what does x-2y =?

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 x-2y= 3-(-2)=5
SVP
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1858
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
Followers: 49

Kudos [?]: 1986 [2] , given: 193

Re: If x+y=2 and x^2 - xy - 10 - 2y^2 = 0, what does x-2y =? [#permalink]

### Show Tags

15 Jul 2014, 22:24
2
KUDOS
$$x^2 - xy - 10 - 2y^2 = 0$$

$$x^2 - 2xy + xy - 2y^2 = 10$$

x(x-2y) + y(x-2y) = 10

(x+y)(x-2y) = 10

$$x-2y = \frac{10}{x+y} = \frac{10}{2} = 5$$

GMAT Club Legend
Joined: 09 Sep 2013
Posts: 13920
Followers: 589

Kudos [?]: 167 [0], given: 0

Re: If x+y=2 and x^2 - xy - 10 - 2y^2 = 0, what does x-2y =? [#permalink]

### Show Tags

18 Aug 2015, 17:43
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
SVP
Joined: 17 Jul 2014
Posts: 2326
Location: United States (IL)
Concentration: Finance, Economics
Schools: Stanford '19 (S)
GMAT 1: 560 Q42 V26
GMAT 2: 550 Q39 V27
GMAT 3: 560 Q43 V24
GMAT 4: 650 Q49 V30
GPA: 3.92
WE: General Management (Transportation)
Followers: 23

Kudos [?]: 270 [0], given: 145

Re: If x+y=2 and x^2 - xy - 10 - 2y^2 = 0, what does x-2y =? [#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 -2xy-20-4y^2 = 0
now add 2 equations
2x^2 -2xy-20-4y^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)(x-y) = 8
we have x+y = 2, that means x-y = 4
x=4+y

4+y+y = 2
2y +4 = 2
y = -1

ok, now get to x:
x-1 = 2 => x=3

x-2y = 3-(-2) = 3+2 = 5.
Manager
Joined: 18 Nov 2013
Posts: 86
Concentration: General Management, Technology
GMAT 1: 690 Q49 V34
Followers: 0

Kudos [?]: 50 [0], given: 63

Re: If x+y=2 and x^2 - xy - 10 - 2y^2 = 0, what does x-2y =? [#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)

$$x-2y =5$$

_________________

_______
- Cheers

+1 kudos if you like

Intern
Joined: 12 Sep 2015
Posts: 1
Followers: 0

Kudos [?]: 0 [0], given: 1

If x+y=2 and x^2 - xy - 10 - 2y^2 = 0, what does x-2y =? [#permalink]

### Show Tags

19 Feb 2017, 01:21
vintage83 wrote:
If x+y=2 and x^2 - xy - 10 - 2y^2 = 0, what does x-2y =?

A. 0
B. 1
C. 2
D. 5
E. 10

I just did the small logic that is x^2-(1)xy-2y^2=10
If I do factor then it will be like (x-2y)(x+y)=10
(x-2y)2=10 .......................As given (x+y)=2
(x-2y)=5

Ans is D

Please correct if i am wrong.
If x+y=2 and x^2 - xy - 10 - 2y^2 = 0, what does x-2y =?   [#permalink] 19 Feb 2017, 01:21
Similar topics Replies Last post
Similar
Topics:
3 If x + y = 2 and x^2 - xy - 10 - 2y^2 = 0, what does x − 2y equal? 4 13 Dec 2015, 05:02
14 If xy≠0 and x^2*y^2-xy=6, which of the following could be y 8 16 Jan 2012, 10:26
12 If xy ≠ 0 and x2y2 – xy = 6, which of the following could be 6 25 Feb 2011, 07:23
16 If 2x^2 –y^2 = 2xy, then (x+y)^2= 9 11 Nov 2010, 21:38
12 If 2x^2 - y^2 = 2xy, then (x+y)^2 = 5 10 May 2010, 16:45
Display posts from previous: Sort by

# If x+y=2 and x^2 - xy - 10 - 2y^2 = 0, what does x-2y =?

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

 Powered by phpBB © phpBB Group and phpBB SEO Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.