GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 21 Sep 2018, 01:10

Close

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
Your Progress

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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

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
Intern
avatar
Joined: 25 Jan 2012
Posts: 4
If x+y=2 and x^2 - xy - 10 - 2y^2 = 0, what does x-2y =?  [#permalink]

Show Tags

New post 28 Feb 2012, 21:12
6
18
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

75% (02:11) correct 25% (02:48) wrong based on 421 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
Most Helpful Expert Reply
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 49276
Re: If x+y=2 and x^2 - xy - 10 - 2y^2 = 0, what does x-2y =?  [#permalink]

Show Tags

New post 28 Feb 2012, 23:12
7
9
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,
Can you please help me solve the equation above

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 \(2(x-2y)-10=0\) --> \(x-2y=5\).

Answer: D.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Most Helpful Community Reply
Current Student
avatar
B
Joined: 23 May 2013
Posts: 188
Location: United States
Concentration: Technology, Healthcare
Schools: Stanford '19 (M)
GMAT 1: 760 Q49 V45
GPA: 3.5
GMAT ToolKit User
Re: If x+y=2 and x^2 - xy - 10 - 2y^2 = 0, what does x-2y =?  [#permalink]

Show Tags

New post 28 May 2014, 07:21
4
2
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.

Answer: D.
General Discussion
Intern
Intern
avatar
Joined: 24 Feb 2012
Posts: 31
Re: If x+y=2 and x^2 - xy - 10 - 2y^2 = 0, what does x-2y =?  [#permalink]

Show Tags

New post 28 Feb 2012, 23:46
1
Very tricky....I confess...I knew there was a simpler route.....but I just did not see it.
Current Student
avatar
Joined: 21 Aug 2010
Posts: 191
Re: If x+y=2 and x^2 - xy - 10 - 2y^2 = 0, what does x-2y =?  [#permalink]

Show Tags

New post 29 Feb 2012, 03:22
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
Intern
avatar
Joined: 25 Jan 2012
Posts: 4
Re: If x+y=2 and x^2 - xy - 10 - 2y^2 = 0, what does x-2y =?  [#permalink]

Show Tags

New post 29 Feb 2012, 07:33
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
User avatar
V
Joined: 02 Sep 2009
Posts: 49276
Re: If x+y=2 and x^2 - xy - 10 - 2y^2 = 0, what does x-2y =?  [#permalink]

Show Tags

New post 03 Jul 2013, 01:24
1
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

_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Verbal Forum Moderator
User avatar
Joined: 10 Oct 2012
Posts: 614
Premium Member
Re: If x+y=2 and x^2 - xy - 10 - 2y^2 = 0, what does x-2y =?  [#permalink]

Show Tags

New post 03 Jul 2013, 02:54
1
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.
_________________

All that is equal and not-Deep Dive In-equality

Hit and Trial for Integral Solutions

Senior Manager
Senior Manager
User avatar
Joined: 13 Jun 2013
Posts: 277
Premium Member
Re: If x+y=2 and x^2 - xy - 10 - 2y^2 = 0, what does x-2y =?  [#permalink]

Show Tags

New post 28 May 2014, 12:26
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
SVP
User avatar
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1834
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 =?  [#permalink]

Show Tags

New post 15 Jul 2014, 23:24
3
\(x^2 - xy - 10 - 2y^2 = 0\)

\(x^2 - 2xy + xy - 2y^2 = 10\)

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

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

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

Answer = D
Board of Directors
User avatar
P
Joined: 17 Jul 2014
Posts: 2684
Location: United States (IL)
Concentration: Finance, Economics
GMAT 1: 650 Q49 V30
GPA: 3.92
WE: General Management (Transportation)
GMAT ToolKit User Premium Member Reviews Badge
Re: If x+y=2 and x^2 - xy - 10 - 2y^2 = 0, what does x-2y =?  [#permalink]

Show Tags

New post 22 Nov 2015, 11:19
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
Manager
User avatar
Joined: 18 Nov 2013
Posts: 81
Concentration: General Management, Technology
GMAT 1: 690 Q49 V34
Premium Member
Re: If x+y=2 and x^2 - xy - 10 - 2y^2 = 0, what does x-2y =?  [#permalink]

Show Tags

New post 20 Mar 2016, 11:54
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)

\(x-2y =5\)

Answer = D
_________________

_______
- Cheers


+1 kudos if you like

Intern
Intern
avatar
B
Joined: 12 Sep 2015
Posts: 3
If x+y=2 and x^2 - xy - 10 - 2y^2 = 0, what does x-2y =?  [#permalink]

Show Tags

New post 19 Feb 2017, 02:21
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.
Intern
Intern
avatar
B
Joined: 14 Jun 2018
Posts: 34
Location: India
Concentration: International Business, Marketing
Re: If x+y=2 and x^2 - xy - 10 - 2y^2 = 0, what does x-2y =?  [#permalink]

Show Tags

New post 06 Sep 2018, 00:17
eaze wrote:
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.

Answer: D.


Hello,
In the second step, shouldn't y=-(x+2) instead of y=x-2 ?
please correct me
Re: If x+y=2 and x^2 - xy - 10 - 2y^2 = 0, what does x-2y =? &nbs [#permalink] 06 Sep 2018, 00:17
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  

Events & Promotions

PREV
NEXT


GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

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®.