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

It is currently 28 Aug 2016, 01:38
GMAT Club Tests

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

In the xy plane line m has the equation 4x + y = k. Line n

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

Hide Tags

1 KUDOS received
Intern
Intern
avatar
Joined: 06 Mar 2012
Posts: 2
Followers: 0

Kudos [?]: 3 [1] , given: 0

In the xy plane line m has the equation 4x + y = k. Line n [#permalink]

Show Tags

New post 06 Mar 2012, 10:37
1
This post received
KUDOS
3
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

71% (02:59) correct 29% (02:36) wrong based on 169 sessions

HideShow timer Statistics

In the xy plane line m has the equation 4x + y = k. Line n passes through the origin and is perpendicular to line m. If point p has the coordinates (r, r+1) and is on both line n and m what is the value of r?

A. -4/3
B. 1/4
C. -4
D. 3/4
E. 4/3

Can anybody help me with this problem?! I really have no idea how to attack this problem..
Thanks!!
[Reveal] Spoiler: OA
Intern
Intern
avatar
Joined: 13 Jan 2012
Posts: 4
Followers: 0

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

Re: Coordinate GGeometry [#permalink]

Show Tags

New post 06 Mar 2012, 11:46
This is an interesting problem, and I haven't solved it either as I am still learning this stuff. so far I've gotten about 3 different wrong answers.

I re wrote the equation of the line M: to Y=-4x + k

Given that N is perpendicular I believe the slope should be the opposite of M's, and it says it passes through the origin so I believe its intercept is 0 so i re wrote line N: to Y=4x + 0

the only point where these two lines share is there intersection where line M=N

-4x+k = 4x+0
k = 8x

x= k/8

plug into either equation to solve for Y = K/2

intersection point is K/8, K/2

since this is equal to P, k/8= R and K/2 = r+1

I think I must have made a mistake because after this point I get various answers that are wrong.

K/8 = K/2 + 1

I solve for K = - 8/3

then I plug back in to solve for R given R= k/8 thus

-8/3 divided by 8

and I get -1/3 = r

an exact difference of positive one... what did i do wrong?
Expert Post
3 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 34457
Followers: 6282

Kudos [?]: 79710 [3] , given: 10022

Re: Coordinate GGeometry [#permalink]

Show Tags

New post 06 Mar 2012, 12:01
3
This post received
KUDOS
Expert's post
3
This post was
BOOKMARKED
In the xy plane line m has the equation 4x + y = k. Line n passes through the origin and is perpendicular to line m. If point p has the coordinates (r, r+1) and is on both line n and m what is the value of r?
A. -4/3
B. 1/4
C. -4
D. 3/4
E. 4/3

The equation of line m is y=-4x+k. Now, since line n is perpendicular to line m, then its slope is negative reciprocal of the slope of line m, so the slope of n is 1/4. Next, as line n passes through the origin (0, 0) and has the slope of 1/4 then its equation is y=1/4*x.

Point (r, r+1) lies on line n means that (r+1)=1/4*r --> r=-4/3.

Answer: A.

For more on this subject check Coordinate Geometry chapter of Math Book: math-coordinate-geometry-87652.html

Hope it helps.
_________________

New to the Math Forum?
Please read this: 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

Intern
Intern
avatar
Joined: 06 Mar 2012
Posts: 2
Followers: 0

Kudos [?]: 3 [0], given: 0

Re: In the xy plane line m has the equation 4x + y = k. Line n [#permalink]

Show Tags

New post 07 Mar 2012, 03:05
Thanks a lot :)

I was stuck at that point, that k=o, because passing through the origin
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 34457
Followers: 6282

Kudos [?]: 79710 [0], given: 10022

Re: In the xy plane line m has the equation 4x + y = k. Line n [#permalink]

Show Tags

New post 29 May 2013, 07:36
Manager
Manager
avatar
Status: Working hard to score better on GMAT
Joined: 02 Oct 2012
Posts: 90
Location: Nepal
Concentration: Finance, Entrepreneurship
GPA: 3.83
WE: Accounting (Consulting)
Followers: 0

Kudos [?]: 137 [0], given: 23

Re: In the xy plane line m has the equation 4x + y = k. Line n [#permalink]

Show Tags

New post 30 May 2013, 23:39
newC wrote:
In the xy plane line m has the equation 4x + y = k. Line n passes through the origin and is perpendicular to line m. If point p has the coordinates (r, r+1) and is on both line n and m what is the value of r?

A. -4/3
B. 1/4
C. -4
D. 3/4
E. 4/3

Can anybody help me with this problem?! I really have no idea how to attack this problem..
Thanks!!


You can approach by calculating slopes of both lines m and n.

As we know both m and n lines are perpendicular; slope m* slope n= -1

slope of m= -4 since 4x=y+k =>(Y=mx+c), where m is slope

now calculate slope of n. as we know line passes through origin (0,0) and (r, r+1)

slope = (y2-y1)/(x2-x1) => (r+1-0)/(r-0) => (r+1)/r

lines are perpendicular; thus we can multiply both slopes

(r+1)/r*-4=-1 gives r= -4/3

Hence Ans is A.

Hit Kudos if you like it... :-D
_________________

Do not forget to hit the Kudos button on your left if you find my post helpful.

GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 09 Sep 2013
Posts: 11107
Followers: 511

Kudos [?]: 134 [0], given: 0

Premium Member
Re: In the xy plane line m has the equation 4x + y = k. Line n [#permalink]

Show Tags

New post 06 Dec 2015, 05:18
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

Expert Post
Math Forum Moderator
avatar
Joined: 20 Mar 2014
Posts: 2636
GMAT 1: 750 Q49 V44
GPA: 3.7
WE: Engineering (Aerospace and Defense)
Followers: 106

Kudos [?]: 1192 [0], given: 786

GMAT ToolKit User Premium Member Reviews Badge
Re: In the xy plane line m has the equation 4x + y = k. Line n [#permalink]

Show Tags

New post 06 Dec 2015, 05:24
newC wrote:
In the xy plane line m has the equation 4x + y = k. Line n passes through the origin and is perpendicular to line m. If point p has the coordinates (r, r+1) and is on both line n and m what is the value of r?

A. -4/3
B. 1/4
C. -4
D. 3/4
E. 4/3

Can anybody help me with this problem?! I really have no idea how to attack this problem..
Thanks!!


Two perpendicular lines with slopes m1 and m2 are such that m1*m2 = -1

Given that lines m and n are perpendicular to each other ---> slope of n = -1/slope of line m = -1/-4 = 1/4

Also, line n passes through (0,0) ---> y = ax+b ---> b=0 and a =1/4 --> equation of line n = y =x/4

Now as point (r,r+1) lies on n , substitute y=r+1 and x=r --> 4(r+1)=r --> 4r+4 = r --> 3r=-4 --> r = -4/3.. A is the correct answer.
_________________

Thursday with Ron updated list as of July 1st, 2015: http://gmatclub.com/forum/consolidated-thursday-with-ron-list-for-all-the-sections-201006.html#p1544515
Rules for Posting in Quant Forums: http://gmatclub.com/forum/rules-for-posting-please-read-this-before-posting-133935.html
Writing Mathematical Formulae in your posts: http://gmatclub.com/forum/rules-for-posting-please-read-this-before-posting-133935.html#p1096628
GMATCLUB Math Book: http://gmatclub.com/forum/gmat-math-book-in-downloadable-pdf-format-130609.html
Everything Related to Inequalities: http://gmatclub.com/forum/inequalities-made-easy-206653.html#p1582891
Inequalities tips: http://gmatclub.com/forum/inequalities-tips-and-hints-175001.html
Debrief, 650 to 750: http://gmatclub.com/forum/650-to-750-a-10-month-journey-to-the-score-203190.html

Expert Post
Senior Manager
Senior Manager
User avatar
Joined: 20 Aug 2015
Posts: 398
Location: India
GMAT 1: 760 Q50 V44
Followers: 20

Kudos [?]: 165 [0], given: 10

Re: In the xy plane line m has the equation 4x + y = k. Line n [#permalink]

Show Tags

New post 07 Dec 2015, 06:43
newC wrote:
In the xy plane line m has the equation 4x + y = k. Line n passes through the origin and is perpendicular to line m. If point p has the coordinates (r, r+1) and is on both line n and m what is the value of r?

A. -4/3
B. 1/4
C. -4
D. 3/4
E. 4/3



Given:
Line m: 4x + y = k Or y = -4x + k
Line n passes through (0,0) and is perpendicular to line m

If two lines are perpendicular, then the product of their slopes = -1

Hence slope of line n = 1/4

Equation of line n:
y - 0 = 1/4(x-0)
y = x/4

Point p lies on the line n
Hence: r+1 = r/4,
4r + 4 = r
r = -4/3
Option A
_________________

Reach out to us at bondwithus@gmatify.com

Image

Re: In the xy plane line m has the equation 4x + y = k. Line n   [#permalink] 07 Dec 2015, 06:43
    Similar topics Author Replies Last post
Similar
Topics:
4 Experts publish their posts in the topic Line m lies in the xy-plane. The y-intercept of line m is -2, and line Bunuel 4 12 May 2015, 04:15
11 Experts publish their posts in the topic In the xy-plane, the line y = k is the perpendicular bisector of the l TARGET730 8 09 Feb 2015, 02:59
9 Experts publish their posts in the topic In the xy-plane, what is the slope of the line with equation Bunuel 9 15 Oct 2012, 04:15
3 Experts publish their posts in the topic In the line xy plane line m has the equation y=3x-8, then monir6000 7 25 Apr 2012, 00:13
29 Experts publish their posts in the topic In the xy plane line k has a positive slope and and cmugeria 16 09 Sep 2010, 10:08
Display posts from previous: Sort by

In the xy plane line m has the equation 4x + y = k. Line n

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


GMAT Club MBA Forum Home| About| 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®.