Find all School-related info fast with the new School-Specific MBA Forum

It is currently 01 Sep 2014, 21:02

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.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

A line with the equation y = px + q is reflected over the

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
Manager
Manager
User avatar
Joined: 04 Apr 2010
Posts: 165
Followers: 1

Kudos [?]: 53 [0], given: 31

GMAT Tests User
A line with the equation y = px + q is reflected over the [#permalink] New post 20 Mar 2011, 16:14
2
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  5% (low)

Question Stats:

30% (00:00) correct 70% (01:06) wrong based on 27 sessions
A line with the equation y = px + q is reflected over the line y = x. Is the reflection of this line parallel to the line y = mx + n?

(1) m = p + 2

(2) m = 3p

I didn't get this question though got the answer right :)
What exactly does reflection mean?
[Reveal] Spoiler: OA

_________________

Consider me giving KUDOS, if you find my post helpful.
If at first you don't succeed, you're running about average. ~Anonymous

Director
Director
avatar
Status: Matriculating
Affiliations: Chicago Booth Class of 2015
Joined: 03 Feb 2011
Posts: 931
Followers: 11

Kudos [?]: 193 [0], given: 123

Reviews Badge
Re: line equation????????? [#permalink] New post 20 Mar 2011, 22:38
S1) insufficient. Slopes are unknown
S2) insufficient
Consider line m to be inclined 60 deg to x axis and line p to be inclined 30 deg to x axis. The reflection of line p about y=x is parallel to line m. The answer to the question is yes.
Consider line m and line p to be parallel to x axis. The reflection of line p about x=y is not prallel to the line m. The answer to the question is no

1) + 2) sufficient
The slopes of the lines are known m=3 and p=1. we can know the angle each line makes with the x axis. And know for sure whether the reflection of line p is symmetrical about the x=y. This can be definitely answered. Sufficient. Hence C

Posted from my mobile device Image

Last edited by gmat1220 on 20 Mar 2011, 23:12, edited 1 time in total.
3 KUDOS received
Manager
Manager
avatar
Joined: 03 Mar 2011
Posts: 94
Location: United States
Schools: Erasmus (S)
GMAT 1: 730 Q51 V37
GPA: 3.9
Followers: 1

Kudos [?]: 89 [3] , given: 12

GMAT Tests User
Re: line equation????????? [#permalink] New post 20 Mar 2011, 23:10
3
This post received
KUDOS
Any monotonous function f(x) which is reflected over the line y=x becomes the function g(x) which is the inverse to f(x). This means f(g(y))=y for all y from the domain and g(f(x))=x for all x from the domain. In case of linear function it is very easy to find the inserve just by changing y to x and x to y.
In our case the inverse x=py+q
y=x/p-q/p

You can read more about inverse functions here
http://en.wikipedia.org/wiki/Inverse_function

If this reflection is paralle to the line y=mx+n, then the slope of two lines are equal, therefore m=1/p. So, finally the question asks whether m=1/p.

(1) says m=p+2, which means that m=1/p only for some particular values of p, so we could not conclude whether the lines are parallel
(2) says m=3p, which means that m=1/p only for some particular values of p, so we could not conclude whether the lines are parallel

(1) and (2) gives us the system
m=p+2
m=3p

from which p+2=3p
p=1 and m=2+1=3

As we could see, m is not equal to 1/p, so these lines are not parallel. Only both statements together are sufficient for the answer.

The answer is C.
_________________

If my post is useful for you not be ashamed to KUDO me!
Let kudo each other!

Director
Director
avatar
Status: Matriculating
Affiliations: Chicago Booth Class of 2015
Joined: 03 Feb 2011
Posts: 931
Followers: 11

Kudos [?]: 193 [0], given: 123

Reviews Badge
Re: line equation????????? [#permalink] New post 20 Mar 2011, 23:15
@bagrettin pls verify my reasoning. Thanks for confirming the answer

Posted from my mobile device Image
1 KUDOS received
Manager
Manager
avatar
Joined: 03 Mar 2011
Posts: 94
Location: United States
Schools: Erasmus (S)
GMAT 1: 730 Q51 V37
GPA: 3.9
Followers: 1

Kudos [?]: 89 [1] , given: 12

GMAT Tests User
Re: line equation????????? [#permalink] New post 21 Mar 2011, 00:21
1
This post received
KUDOS
Hello, gmat1220 :)

Your reasoning is right!

In S1. Just to be more precise, let say that correspondence between slopes p and p+2 are different for the different values of p, therefore the answer on the question will be different too (for exact equation, linking inverse function see my post)

In S2 your example with 60 and 30 degrees corresponds to m=3p. The line which is inclined 60 degrees to x axis has the slope of 3^0.5 (tg 60), while the line with 30 degrees to x axis has the slope 1/3^0.5 (tg 30), so m=3p. Again since y=x is inclined at 45 degrees to Ox, this lines are symmetrical to the y=x.

If both lines have the slope of 0, then m=3p, while the reflection will be vertical line with the slope equal to infinity.
_________________

If my post is useful for you not be ashamed to KUDO me!
Let kudo each other!

Director
Director
avatar
Status: Matriculating
Affiliations: Chicago Booth Class of 2015
Joined: 03 Feb 2011
Posts: 931
Followers: 11

Kudos [?]: 193 [0], given: 123

Reviews Badge
Re: line equation????????? [#permalink] New post 21 Mar 2011, 06:20
Hello bagrettin
Your explanation rocks!!!!! Thanks so much.

Posted from my mobile device Image
Manager
Manager
avatar
Joined: 03 Mar 2011
Posts: 94
Location: United States
Schools: Erasmus (S)
GMAT 1: 730 Q51 V37
GPA: 3.9
Followers: 1

Kudos [?]: 89 [0], given: 12

GMAT Tests User
Re: line equation????????? [#permalink] New post 21 Mar 2011, 12:03
Hello, gmat1220!

Happy to help you) You are always welcome! ;)
_________________

If my post is useful for you not be ashamed to KUDO me!
Let kudo each other!

Manager
Manager
User avatar
Joined: 04 Apr 2010
Posts: 165
Followers: 1

Kudos [?]: 53 [0], given: 31

GMAT Tests User
Re: line equation????????? [#permalink] New post 21 Mar 2011, 15:21
Great explanation bagrettin !
Thanks to gmat1220 also.
_________________

Consider me giving KUDOS, if you find my post helpful.
If at first you don't succeed, you're running about average. ~Anonymous

Intern
Intern
avatar
Joined: 16 Sep 2011
Posts: 1
Followers: 0

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

Re: line equation????????? [#permalink] New post 24 Oct 2011, 03:45
The explanation is indeed splendid I was searching for some more on equations of line when I found this link on tutorvista which was a great help i think you should also check it out.
Senior Manager
Senior Manager
avatar
Joined: 06 Aug 2011
Posts: 409
Followers: 2

Kudos [?]: 58 [0], given: 82

A line with the equation y = px + q is reflected over the li [#permalink] New post 02 Oct 2012, 00:19
3
This post was
BOOKMARKED
A line with the equation y = px + q is reflected over the line y = x. Is the reflection of this line parallel to the line y = mx + n?

(1) m = p + 2

(2) m = 3p


I know this question has been discussed earlier..bt that discussion didnt help me out..thats y have made new topic..:)..
_________________

Bole So Nehal.. Sat Siri Akal.. Waheguru ji help me to get 700+ score !

3 KUDOS received
BSchool Thread Master
User avatar
Status: If you think you can, then eventually you WILL!
Joined: 05 Apr 2011
Posts: 430
Location: India
Concentration: Finance, Marketing
Schools: XLRI (A)
GMAT 1: 570 Q49 V19
GMAT 2: 700 Q51 V31
GPA: 3
WE: Information Technology (Computer Software)
Followers: 57

Kudos [?]: 234 [3] , given: 41

GMAT Tests User Premium Member
Re: A line with the equation y = px + q is reflected over the li [#permalink] New post 02 Oct 2012, 18:13
3
This post received
KUDOS
1
This post was
BOOKMARKED
A line with the equation y = px + q is reflected over the line y = x. Is the reflection of this line parallel to the line y = mx + n?

(1) m = p + 2

(2) m = 3p

When a line is reflected around y=x then the equation of the reflected line is got by swapping the x and y of the original equation.
So, equation of the reflection of the line y=px + q will be x = py + q

So, for this line to be parallel to y = mx + n we just need to make sure that the slope of the two lines are equal
i.e. 1/p = m

STAT1
m = p + 2
But we cannot say whether m=1/p will be true or not. Proof is below.
Trying m =1/p
we get
1/p = p + 2
p^2 + 2p - 1 =0
p = { -2 +- sqrt(4 + 4) }/2 = { -2 + 4sqrt2 } /2
But there can be many other values of p for which m = p+2 will be true but m = 1/p will not be true.
So, INSUFFICIENT

STAT2
m = 3p
But we cannot say whether m=1/p will be true or not. Proof is below.
Trying m = 1/p
1/p = 3p
=> p^2 = 1/3
But there can be many other values of p for which m = p+2 will be true but m = 1/p will not be true.
So, INSUFFICIENT

Taking both together we have
m = p+2 and m=3p
=> 3p = p+2
=> p = 1

So, m = p+2 = 3
And 1/p = 1
Clearly m is not equal to 1/p. So, lines are not parallel.

So, Answer will be C.
Hope it helps!
_________________

ankit
you must believe

How to start GMAT preparations?
How to Improve Quant Score?
gmatclub topic tags
Check out my GMAT debrief
Thursdays with Ron link
Looking for a Quant tutor? Check out my post for the same!

Combined Formula Sheet :
Number Properties || Word Problems and PnC || Equations, Inequalities || Geometry

How to Solve :
Statistics || Reflection of a line || Remainder Problems


Last edited by nktdotgupta on 02 Oct 2012, 18:57, edited 1 time in total.
Senior Manager
Senior Manager
User avatar
Joined: 11 May 2011
Posts: 376
Location: US
Followers: 2

Kudos [?]: 61 [0], given: 46

Re: A line with the equation y = px + q is reflected over the li [#permalink] New post 02 Oct 2012, 19:33
@nktdotgupta - Thx for the explanation but i've another question on this.
What if -
1. A line with the equation y = px + q is reflected over the line y = 2x, How shall we approach this question?
2. A line with the equation y = px + q is reflected over the line y = 5, How shall we approach this question?
_________________

-----------------------------------------------------------------------------------------
What you do TODAY is important because you're exchanging a day of your life for it!
-----------------------------------------------------------------------------------------

1 KUDOS received
BSchool Thread Master
User avatar
Status: If you think you can, then eventually you WILL!
Joined: 05 Apr 2011
Posts: 430
Location: India
Concentration: Finance, Marketing
Schools: XLRI (A)
GMAT 1: 570 Q49 V19
GMAT 2: 700 Q51 V31
GPA: 3
WE: Information Technology (Computer Software)
Followers: 57

Kudos [?]: 234 [1] , given: 41

GMAT Tests User Premium Member
Re: A line with the equation y = px + q is reflected over the li [#permalink] New post 02 Oct 2012, 20:40
1
This post received
KUDOS
Hi,

To find the equation of the reflected line just keep in mind the following things:--

1. Each and every point on the reflected line has the same distance from the line on which the reflection happened as the corresponding point on the original line.
2. The line on which reflection happens is the perpendicular bisector of the line joining a point on the original line and the corresponding point on the reflected line.

So, to find the equation of the reflected line you need to find two points.
One point you can get by finding the point of intersection of the original line and the line on which the reflection happened.
To find the other point you can take any point on the original line and drop a perpendicular to the line on which reflection has to happen. And find the point of the intersection of the line on which the reflection has to happen and the perpendicular drawn just now.
Now, the point of intersection which we got just now is the mid point of the point on the original line and the point on the reflected line. So, we can find the point on the reflected line too.

Will give an example : ( Figure attached )
Suppose we are given the equation of line l and we have to find the reflection of l on line m
line n is the reflected line whose equation we need to find.
We can find one point (O) by solving for lines l and m
Now to find one more point on line n (C(x2,y2)):
Take a point A(x,y) on line l and draw a perpendicular to line m (point B)
Now , we know the slope of line m so we can find the slope of any line perpendicular to line m and we have one point (A) through which that perpendicular is passing so we can find equation of that perpendicular and hence we can find point B (x1, y1)
Since, B is the midpoint of AC (since the line on which reflection happens is the perpendicular bisector of any two corresponding lines on the original and the reflected line)
So,
x1 = (x+ x2) /2
and
y1 = (y + y2)/2
So, we can find x2,y2 and hence point C
Once we have point C then we can find equation of line n as we have two point O and C

Now coming to your doubt:
What if -
1. A line with the equation y = px + q is reflected over the line y = 2x, How shall we approach this question?
2. A line with the equation y = px + q is reflected over the line y = 5, How shall we approach this question?

For the 1st one i will go with the approach mentioned above.
For the second one since the line is y=5. So the X co-ordinate of the corresponding point on the reflected line will remain same but for finding the y co-ordinate i will follow the procedure mentioned above.

Hope it helps!
Attachments

File comment: File attached
image.JPG
image.JPG [ 14.48 KiB | Viewed 2062 times ]


_________________

ankit
you must believe

How to start GMAT preparations?
How to Improve Quant Score?
gmatclub topic tags
Check out my GMAT debrief
Thursdays with Ron link
Looking for a Quant tutor? Check out my post for the same!

Combined Formula Sheet :
Number Properties || Word Problems and PnC || Equations, Inequalities || Geometry

How to Solve :
Statistics || Reflection of a line || Remainder Problems

Senior Manager
Senior Manager
avatar
Joined: 06 Aug 2011
Posts: 409
Followers: 2

Kudos [?]: 58 [0], given: 82

Re: A line with the equation y = px + q is reflected over the li [#permalink] New post 02 Oct 2012, 22:34
Thanks alot..!!

i got it now..!
_________________

Bole So Nehal.. Sat Siri Akal.. Waheguru ji help me to get 700+ score !

SVP
SVP
User avatar
Joined: 06 Sep 2013
Posts: 1629
Location: United States
Concentration: Finance
GMAT 1: 710 Q48 V39
WE: Corporate Finance (Investment Banking)
Followers: 11

Kudos [?]: 157 [0], given: 254

GMAT ToolKit User
Re: A line with the equation y = px + q is reflected over the li [#permalink] New post 28 Nov 2013, 08:22
nktdotgupta wrote:
A line with the equation y = px + q is reflected over the line y = x. Is the reflection of this line parallel to the line y = mx + n?

(1) m = p + 2

(2) m = 3p

When a line is reflected around y=x then the equation of the reflected line is got by swapping the x and y of the original equation.
So, equation of the reflection of the line y=px + q will be x = py + q

So, for this line to be parallel to y = mx + n we just need to make sure that the slope of the two lines are equal
i.e. 1/p = m

STAT1
m = p + 2
But we cannot say whether m=1/p will be true or not. Proof is below.
Trying m =1/p
we get
1/p = p + 2
p^2 + 2p - 1 =0
p = { -2 +- sqrt(4 + 4) }/2 = { -2 + 4sqrt2 } /2
But there can be many other values of p for which m = p+2 will be true but m = 1/p will not be true.
So, INSUFFICIENT

STAT2
m = 3p
But we cannot say whether m=1/p will be true or not. Proof is below.
Trying m = 1/p
1/p = 3p
=> p^2 = 1/3
But there can be many other values of p for which m = p+2 will be true but m = 1/p will not be true.
So, INSUFFICIENT

Taking both together we have
m = p+2 and m=3p
=> 3p = p+2
=> p = 1

So, m = p+2 = 3
And 1/p = 1
Clearly m is not equal to 1/p. So, lines are not parallel.

So, Answer will be C.
Hope it helps!


You say that for two lines to be parallel their product should be 1.
I don't get it, I thought that for two lines to be parallel they had to have the same slope.
So in this case m = p

Please clarify
Thanks
Cheers
J :)
Moderator
Moderator
User avatar
Joined: 25 Apr 2012
Posts: 620
Location: India
GPA: 3.21
WE: Business Development (Other)
Followers: 15

Kudos [?]: 277 [0], given: 654

Premium Member CAT Tests
Re: A line with the equation y = px + q is reflected over the li [#permalink] New post 29 Nov 2013, 02:56
jlgdr wrote:
nktdotgupta wrote:
A line with the equation y = px + q is reflected over the line y = x. Is the reflection of this line parallel to the line y = mx + n?

(1) m = p + 2

(2) m = 3p

When a line is reflected around y=x then the equation of the reflected line is got by swapping the x and y of the original equation.
So, equation of the reflection of the line y=px + q will be x = py + q

So, for this line to be parallel to y = mx + n we just need to make sure that the slope of the two lines are equal
i.e. 1/p = m

STAT1
m = p + 2
But we cannot say whether m=1/p will be true or not. Proof is below.
Trying m =1/p
we get
1/p = p + 2
p^2 + 2p - 1 =0
p = { -2 +- sqrt(4 + 4) }/2 = { -2 + 4sqrt2 } /2
But there can be many other values of p for which m = p+2 will be true but m = 1/p will not be true.
So, INSUFFICIENT

STAT2
m = 3p
But we cannot say whether m=1/p will be true or not. Proof is below.
Trying m = 1/p
1/p = 3p
=> p^2 = 1/3
But there can be many other values of p for which m = p+2 will be true but m = 1/p will not be true.
So, INSUFFICIENT

Taking both together we have
m = p+2 and m=3p
=> 3p = p+2
=> p = 1

So, m = p+2 = 3
And 1/p = 1
Clearly m is not equal to 1/p. So, lines are not parallel.

So, Answer will be C.
Hope it helps!


You say that for two lines to be parallel their product should be 1.
I don't get it, I thought that for two lines to be parallel they had to have the same slope.
So in this case m = p

Please clarify
Thanks
Cheers
J :)



For 2 lines to be parallel, their slopes must be equal and for 2 lines to be perpendicular, the product of slopes should = -1
Here the question asked whether the slope of the reflection of line y=px+q which isx=py+q parallel to line y= mx+n

So the slope of reflected line x=py+q ---------> 1/p

ie. is 1/p= m or in this case is pm= 1
_________________


“If you can't fly then run, if you can't run then walk, if you can't walk then crawl, but whatever you do you have to keep moving forward.”

SVP
SVP
User avatar
Joined: 09 Sep 2013
Posts: 2240
Followers: 186

Kudos [?]: 37 [0], given: 0

Premium Member
Re: A line with the equation y = px + q is reflected over the [#permalink] New post 18 Aug 2014, 02:59
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.
_________________

GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

Re: A line with the equation y = px + q is reflected over the   [#permalink] 18 Aug 2014, 02:59
    Similar topics Author Replies Last post
Similar
Topics:
3 Experts publish their posts in the topic Line Q has the equation 5y – 3x = 45. If Line S is perpendicular to Q mikemcgarry 6 29 Aug 2014, 15:58
A line with the equation y = px + q is reflected over the li sanjoo 0 29 Nov 2013, 02:56
2 Experts publish their posts in the topic Does the equation y = (x – p)(x – q) intercept the x-axis at alchemist009 5 09 Jun 2012, 16:24
8 Experts publish their posts in the topic If one root of x^2+px+12=0 is 4, and the equation x^2+px+q=0 feruz77 7 09 Dec 2010, 06:39
A,B are roots of equation (x)(x)-px+q=0. A,C are roots of smcgrath12 3 30 Oct 2004, 12:11
Display posts from previous: Sort by

A line with the equation y = px + q is reflected over the

  Question banks Downloads My Bookmarks Reviews Important topics  


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

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®.