Last visit was: 14 Dec 2024, 10:56 It is currently 14 Dec 2024, 10:56
Home
GMAT
Messages
Tests
Schools
Reviews
Social
Chat
My Profile
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.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel
Back to Forum
Create Topic
avatar
d.rouleau
avatar
Joined: 26 Dec 2013
Last visit: 18 May 2014
Posts: 3
Own Kudos:
10
 []
Given Kudos: 6
Posts: 3
Kudos: 10
 []
In the rectangular coordinate system, lines m and n intersec Updated on: 14 May 2014, 00:36
Originally posted by d.rouleau on 13 May 2014, 15:49.
Last edited by Bunuel on 14 May 2014, 00:36, edited 1 time in total.
RENAMED THE TOPIC.
2
Kudos
Add Kudos
8
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

25% (medium)

Question Stats:

75% (01:24) correct 25% (01:18) wrong based on 353 sessions

History

Date
Time
Result
Not Attempted Yet
In the rectangular coordinate system, lines m and n intersect at the origin. Is line m perpendicular to line n?

(1) Line n passes through the point (-a, -a), where a ≠ 0, and line m has a slope of -1.

(2) The product of the slope of line m and the slope of line n is -1.


1) Is obviously sufficient.

2) Say

Line M : y=0,5x
Line N : y=-2x

Product of both slope = -1

But these are NOT perpendicular...

Am I drunk?

Thanks,

Regards,

David

** And obviously if it's m=x and n=-x, it yields -1 as well and the answer would be that they're perpendicular, thus since it's a maybe, it wouldn't be sufficient... **
ShowHide Answer
Official Answer
D
avatar
ershovici
avatar
Joined: 29 Jan 2014
Last visit: 10 Feb 2015
Posts: 11
Own Kudos:
31
 []
Given Kudos: 4
Location: United States
Concentration: General Management, Entrepreneurship
Schools: Babson '17 (A$)
GMAT 1: 720 Q48 V40
GPA: 3.8
Schools: Babson '17 (A$)
GMAT 1: 720 Q48 V40
Posts: 11
Kudos: 31
 []
In the rectangular coordinate system, lines m and n intersec 13 May 2014, 18:09
3
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Ok, so we have two lines m and n

Two lines are perpendicular if the product of their slopes is -1 !!!

Statement 1 - states that "Line n passes through the point (-a, -a), where a ≠ 0," and also through origin (since two lines intersect at origin). Since for every decrease in X coordinate, Y coordinate decreases by the same amount, and the line comes through the quadrant 3 - we know that the slope of the line is 1. The second line has a slope of -1. So, 1*(-1) = -1 - Sufficient

Statement 2 : product of slopes of two lines is -1. Sufficient.

Ans D.

PS. check this book to refresh some basic concepts. gmat-math-book-87417.html
avatar
d.rouleau
avatar
Joined: 26 Dec 2013
Last visit: 18 May 2014
Posts: 3
Own Kudos:
10
Given Kudos: 6
Posts: 3
Kudos: 10
In the rectangular coordinate system, lines m and n intersec 13 May 2014, 19:12
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Hey ershovici,

Thanks for the reply,

Indeed, I get the point.

But perpendicular slopes are 90 degree from each other, right?

But if m:-2x and n:0,5x, the product is still -1 but they aren't standing at 90 degree, right?
User avatar
gmatacequants
User avatar
Joined: 13 May 2014
Last visit: 03 Sep 2019
Posts: 26
Own Kudos:
246
 []
Given Kudos: 1
Concentration: General Management, Strategy
Posts: 26
Kudos: 246
 []
In the rectangular coordinate system, lines m and n intersec 14 May 2014, 00:11
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
d.rouleau
Hey ershovici,

Thanks for the reply,

Indeed, I get the point.

But perpendicular slopes are 90 degree from each other, right?

But if m:-2x and n:0,5x, the product is still -1 but they aren't standing at 90 degree, right?

Hey d.rouleau
No, they are.
suppose, the eqn for two lines :
i) Line M:Y = m.X + c1 ,
ii) Line N: Y = n.X + c2

so they will be making 90 degree with each other, if m*n = -1.

Taking the lines as
Y = -2x + c1
Y = 0.5x + c2 ; so the slope product = -1 which makes them perpendicular to each other.
Depending on c1 and c2 , the point of intersection would vary.
IF c1=0 and c2=0,in your case, they would intersect at origin; otherwise at some different point other than the origin.
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 14 Dec 2024
Posts: 97,877
Own Kudos:
685,841
 []
Given Kudos: 88,270
Products:
GMAT Club Tests Forum Quiz
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 97,877
Kudos: 685,841
 []
In the rectangular coordinate system, lines m and n intersec 14 May 2014, 00:39
4
Kudos
Add Kudos
Bookmarks
Bookmark this Post
d.rouleau
In the rectangular coordinate system, lines m and n intersect at the origin. Is line m perpendicular to line n?

(1) Line n passes through the point (-a, -a), where a ≠ 0, and line m has a slope of -1.

(2) The product of the slope of line m and the slope of line n is -1.


1) Is obviously sufficient.

2) Say

Line M : y=0,5x
Line N : y=-2x

Product of both slope = -1

But these are NOT perpendicular...

Am I drunk?

Thanks,

Regards,

David

** And obviously if it's m=x and n=-x, it yields -1 as well and the answer would be that they're perpendicular, thus since it's a maybe, it wouldn't be sufficient... **

For one line to be perpendicular to another, the relationship between their slopes has to be negative reciprocal \(-\frac{1}{m}\). In other words, the two lines are perpendicular if and only if the product of their slopes is \(-1\).

So, line y=0.5x and y=-2x must be perpendicular because the product of the slopes is 0.5*(-2)=-1. And indeed they are:
Attachment:
graph.png
graph.png [ 8.49 KiB | Viewed 6855 times ]

Theory on Coordinate Geometry: math-coordinate-geometry-87652.html

All DS Coordinate Geometry Problems to practice: search.php?search_id=tag&tag_id=41
All PS Coordinate Geometry Problems to practice: search.php?search_id=tag&tag_id=62

Hope this helps.
avatar
d.rouleau
avatar
Joined: 26 Dec 2013
Last visit: 18 May 2014
Posts: 3
Own Kudos:
10
Given Kudos: 6
Posts: 3
Kudos: 10
In the rectangular coordinate system, lines m and n intersec 14 May 2014, 04:41
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Hey guys,

Thanks for the reply,

The concept is totally legit, the main reason is that I was making the graph with google... I just realised that google did not use a coma as a separator. Therefore it is obvious that it wasn't perpendicular.

I think I just needed some sleep haha.

Thanks again,

Regards,

D
User avatar
mbaapp1234
User avatar
Joined: 23 Dec 2013
Last visit: 05 Jul 2019
Posts: 85
Own Kudos:
84
Given Kudos: 23
Location: United States (CA)
Schools: HBS '20 (D) Stanford '20 (D) Yale '21 (A$) Tuck '21 (A) Wharton '21 (A) Sloan '21 (A)
GMAT 1: 710 Q45 V41
GMAT 2: 760 Q49 V44
GPA: 3.76
Products:
My Reviews
Schools: HBS '20 (D) Stanford '20 (D) Yale '21 (A$) Tuck '21 (A) Wharton '21 (A) Sloan '21 (A)
GMAT 2: 760 Q49 V44
Posts: 85
Kudos: 84
In the rectangular coordinate system, lines m and n intersec 21 May 2017, 19:39
Kudos
Add Kudos
Bookmarks
Bookmark this Post
d.rouleau
In the rectangular coordinate system, lines m and n intersect at the origin. Is line m perpendicular to line n?

(1) Line n passes through the point (-a, -a), where a ≠ 0, and line m has a slope of -1.

(2) The product of the slope of line m and the slope of line n is -1.


1) Is obviously sufficient.

2) Say

Line M : y=0,5x
Line N : y=-2x

Product of both slope = -1

But these are NOT perpendicular...

Am I drunk?

Thanks,

Regards,

David

** And obviously if it's m=x and n=-x, it yields -1 as well and the answer would be that they're perpendicular, thus since it's a maybe, it wouldn't be sufficient... **

Statement 1: We know two points of line N and we know the slope of line M. Recall that two lines are perpendicular to each other if their slopes are negative reciprocals of each other. So we are trying to prove that slope of m * slope of n = -1.

Here we know that the slope of N is A/A =1 because N passes through (0,0) and (-A, -A). We can use the slope formula to determine that (-A-0)/(-A-0) is = 1. Meanwhile we are told that the slope of M is -1. So the two are negative reciprocals of each other, and the statement is sufficient.

Statement 2: We know that the two are negative reciprocals of each other. So they must be perpendicular. Sufficient.
User avatar
Nunuboy1994
User avatar
Joined: 12 Nov 2016
Last visit: 24 Apr 2019
Posts: 564
Own Kudos:
119
Given Kudos: 167
Location: United States
Schools: Yale '18
GMAT 1: 650 Q43 V37
GRE 1: Q157 V158
GPA: 2.66
Schools: Yale '18
GMAT 1: 650 Q43 V37
GRE 1: Q157 V158
Posts: 564
Kudos: 119
In the rectangular coordinate system, lines m and n intersec 17 Jun 2017, 09:21
Kudos
Add Kudos
Bookmarks
Bookmark this Post
d.rouleau
In the rectangular coordinate system, lines m and n intersect at the origin. Is line m perpendicular to line n?

(1) Line n passes through the point (-a, -a), where a ≠ 0, and line m has a slope of -1.

(2) The product of the slope of line m and the slope of line n is -1.


1) Is obviously sufficient.

2) Say

Line M : y=0,5x
Line N : y=-2x

Product of both slope = -1

But these are NOT perpendicular...

Am I drunk?

Thanks,

Regards,

David

** And obviously if it's m=x and n=-x, it yields -1 as well and the answer would be that they're perpendicular, thus since it's a maybe, it wouldn't be sufficient... **

Statement 1

Plug in a simple value
(-1 , -1)

In order for this line to pass through the origin the slope must be 1- the negative reciprocal of 1 is -1 which is given by m

Suff

Statement 2

The product of a negative reciprocal and its reciprocal simply -1

Suff

D
User avatar
bumpbot
User avatar
Non-Human User
Joined: 09 Sep 2013
Last visit: 04 Jan 2021
Posts: 35,820
Own Kudos:
930
Posts: 35,820
Kudos: 930
In the rectangular coordinate system, lines m and n intersec 08 Apr 2022, 10:45
Kudos
Add Kudos
Bookmarks
Bookmark this Post
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.
Moderator:
Bunuel
Math Expert
97877 posts