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

 It is currently 06 Dec 2019, 10:38

### 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

# The straight lines given by the equation 2x^2=2y^2-3xy are:

Author Message
TAGS:

### Hide Tags

GMATH Teacher
Status: GMATH founder
Joined: 12 Oct 2010
Posts: 935
The straight lines given by the equation 2x^2=2y^2-3xy are:  [#permalink]

### Show Tags

21 Mar 2019, 13:19
00:00

Difficulty:

55% (hard)

Question Stats:

56% (02:28) correct 44% (02:07) wrong based on 27 sessions

### HideShow timer Statistics

GMATH practice exercise (Quant Class 20)

The straight lines given by the equation $$2{x^2} = 2{y^2} - 3xy$$ are:

(A) parallel
(B) intersecting and they form a 30-degrees angle
(C) intersecting and they form a 45-degrees angle
(D) intersecting and they form a 60-degrees angle
(E) intersecting and they form a 90-degrees angle

_________________
Fabio Skilnik :: GMATH method creator (Math for the GMAT)
Our high-level "quant" preparation starts here: https://gmath.net
GMATH Teacher
Status: GMATH founder
Joined: 12 Oct 2010
Posts: 935
Re: The straight lines given by the equation 2x^2=2y^2-3xy are:  [#permalink]

### Show Tags

21 Mar 2019, 14:47
1
fskilnik wrote:
GMATH practice exercise (Quant Class 20)

The straight lines given by the equation $$2{x^2} = 2{y^2} - 3xy$$ are:

(A) parallel
(B) intersecting and they form a 30-degrees angle
(C) intersecting and they form a 45-degrees angle
(D) intersecting and they form a 60-degrees angle
(E) intersecting and they form a 90-degrees angle

$$?\,\,:\,\,{\rm{lines}}\,\,{\rm{relative}}\,\,{\rm{position}}$$

$$2{x^2} = 2{y^2} - 3xy\,\,\,\, \Leftrightarrow \,\,\,\,2{x^2} - xy = 2{y^2} - 4xy\,\,\,\, \Leftrightarrow$$

$$\Leftrightarrow \,\,\,\,x\left( {2x - y} \right) = - 2y\left( { - y + 2x} \right)\,\,\,\, \Leftrightarrow \,\,\,\,\left( {2x - y} \right)\left( {x + 2y} \right) = 0$$

$$\left( {2x - y} \right)\left( {x + 2y} \right) = 0\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\left\{ \matrix{ \,2x - y = 0 \hfill \cr \,\,{\rm{or}} \hfill \cr \,x + 2y = 0 \hfill \cr} \right.\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\left\{ \matrix{ \,y = 2x\,\,\,\,\left( {{\rm{slope}} = 2} \right) \hfill \cr \,\,{\rm{or}} \hfill \cr \,y = - {x \over 2}\,\,\,\,\left( {{\rm{slope}} = - {1 \over 2}} \right) \hfill \cr} \right.\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\left( {\rm{E}} \right)$$

We follow the notations and rationale taught in the GMATH method.

Regards,
Fabio.
_________________
Fabio Skilnik :: GMATH method creator (Math for the GMAT)
Our high-level "quant" preparation starts here: https://gmath.net
SVP
Joined: 26 Mar 2013
Posts: 2343
Re: The straight lines given by the equation 2x^2=2y^2-3xy are:  [#permalink]

### Show Tags

21 Mar 2019, 17:44
fskilnik wrote:
fskilnik wrote:
GMATH practice exercise (Quant Class 20)

The straight lines given by the equation $$2{x^2} = 2{y^2} - 3xy$$ are:

(A) parallel
(B) intersecting and they form a 30-degrees angle
(C) intersecting and they form a 45-degrees angle
(D) intersecting and they form a 60-degrees angle
(E) intersecting and they form a 90-degrees angle

$$?\,\,:\,\,{\rm{lines}}\,\,{\rm{relative}}\,\,{\rm{position}}$$

$$2{x^2} = 2{y^2} - 3xy\,\,\,\, \Leftrightarrow \,\,\,\,2{x^2} - xy = 2{y^2} - 4xy\,\,\,\, \Leftrightarrow$$

$$\Leftrightarrow \,\,\,\,x\left( {2x - y} \right) = - 2y\left( { - y + 2x} \right)\,\,\,\, \Leftrightarrow \,\,\,\,\left( {2x - y} \right)\left( {x + 2y} \right) = 0$$

$$\left( {2x - y} \right)\left( {x + 2y} \right) = 0\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\left\{ \matrix{ \,2x - y = 0 \hfill \cr \,\,{\rm{or}} \hfill \cr \,x + 2y = 0 \hfill \cr} \right.\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\left\{ \matrix{ \,y = 2x\,\,\,\,\left( {{\rm{slope}} = 2} \right) \hfill \cr \,\,{\rm{or}} \hfill \cr \,y = - {x \over 2}\,\,\,\,\left( {{\rm{slope}} = - {1 \over 2}} \right) \hfill \cr} \right.\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\left( {\rm{E}} \right)$$

We follow the notations and rationale taught in the GMATH method.

Regards,
Fabio.

Hi,
Is not it the equation above second degree that does present a line? As I know, an equation of line is first degree. Can you help please with more details?
GMATH Teacher
Status: GMATH founder
Joined: 12 Oct 2010
Posts: 935
The straight lines given by the equation 2x^2=2y^2-3xy are:  [#permalink]

### Show Tags

21 Mar 2019, 18:03
Mo2men wrote:

Hi,
Is not it the equation above second degree that does present a line? As I know, an equation of line is first degree. Can you help please with more details?

Hi Mo2men,

Thank you for your interest in our problem and in my solution.

I will not go into many details about the relationship between lines and first-degree equations, because all that it is needed to know (in GMAT´s scope) is contained in our course.

On the other hand, please notice that the set of points (x,y) in the rectangular coordinate system, associated with the solution set of the second-degree equation presented in the question stem, is exactly the reunion of TWO intersecting lines, not just one line.

In other words, your intuition/knowledge is not refuted: the second-degree equation presented in the question stem is NOT related to a SINGLE straight line!

Regards and success in your studies,
Fabio.
_________________
Fabio Skilnik :: GMATH method creator (Math for the GMAT)
Our high-level "quant" preparation starts here: https://gmath.net
The straight lines given by the equation 2x^2=2y^2-3xy are:   [#permalink] 21 Mar 2019, 18:03
Display posts from previous: Sort by