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

It is currently 31 Jul 2015, 22:10
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

If line L passes through

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
Forum Moderator
Forum Moderator
User avatar
Status: mission completed!
Joined: 02 Jul 2009
Posts: 1420
GPA: 3.77
Followers: 172

Kudos [?]: 659 [0], given: 618

GMAT ToolKit User Premium Member Reviews Badge
If line L passes through [#permalink] New post 31 Mar 2011, 04:45
00:00
A
B
C
D
E

Difficulty:

(N/A)

Question Stats:

25% (00:00) correct 75% (00:23) wrong based on 4 sessions
157. If line L passes through point (m, n) and
(– m, – n), where m and n are not 0, which of the following must be true?
I. The slope of L is positive
II. The slope of L is negative
III. L exactly passes through 2 quadrants
(A) I only
(B) II only
(C) III only
(D) I and II only
(E) II and III only
[Reveal] Spoiler: OA

_________________

Audaces fortuna juvat!

GMAT Club Premium Membership - big benefits and savings

2 KUDOS received
Math Forum Moderator
avatar
Joined: 20 Dec 2010
Posts: 2028
Followers: 140

Kudos [?]: 1181 [2] , given: 376

Re: If line L passes through [#permalink] New post 31 Mar 2011, 05:20
2
This post received
KUDOS
Pkit wrote:
157. If line L passes through point (m, n) and
(– m, – n), where m and n are not 0, which of the following must be true?
I. The slope of L is positive
II. The slope of L is negative
III. L exactly passes through 2 quadrants
(A) I only
(B) II only
(C) III only
(D) I and II only
(E) II and III only


Equation of the line with slope m passing through point \((x_1,y_1)\) \(&\) \((x_2,y_2)\)
\((y-y_1)=m(x-x_1)=\frac{y_2-y_1}{x_2-x_1}(x-x_1)\)

We have the line that is passing through \((m,n)\) \(&\) \((-m,-n)\)

\(Slope=\frac{-n-n}{-m-m}=\frac{n}{m}\)

Equation of the line will be:
\(y-n=\frac{n}{m}(x-m)\)
\(y-n=\frac{n}{m}x-n\)
\(y=\frac{n}{m}x\)

Thus we know that this line passes through the origin as the y-intercept is 0. This makes III true.

If we put, n=1 and m=1
\(y=x\); this line has a positive slope. We can count II out.

Put n=-1 and m=1
\(y=-x\); this line has negative slope. We can count I out.

Ans: "C"
_________________

~fluke

GMAT Club Premium Membership - big benefits and savings

SVP
SVP
avatar
Joined: 16 Nov 2010
Posts: 1678
Location: United States (IN)
Concentration: Strategy, Technology
Followers: 31

Kudos [?]: 364 [0], given: 36

Premium Member Reviews Badge
Re: If line L passes through [#permalink] New post 31 Mar 2011, 05:28
Let (m,n) = (2,3)

(-m,-n) = (-2,-3)

Slope = (3+3)/(2+2) = 6/4 = 3/2

So II may not be true


Let (m,n) = (2,-3) then (-m,-n) = (-2,3)

So slope = (3 +3)/(-2-2) = -3/2

so I may not be true


So such a line would be -> (y - 3) = 3/2(x - 2)

=> 2y - 6 = 3x - 6

=> 2y - 3x = 0, hence no x or y intercept, so it passes through origin.

III is true.

Answer - C
_________________

Formula of Life -> Achievement/Potential = k * Happiness (where k is a constant)

GMAT Club Premium Membership - big benefits and savings

SVP
SVP
avatar
Joined: 16 Nov 2010
Posts: 1678
Location: United States (IN)
Concentration: Strategy, Technology
Followers: 31

Kudos [?]: 364 [0], given: 36

Premium Member Reviews Badge
Re: If line L passes through [#permalink] New post 31 Mar 2011, 05:35
@fluke and @PKit, should this be moved to PS forum, doesn't look like a DS question.
_________________

Formula of Life -> Achievement/Potential = k * Happiness (where k is a constant)

GMAT Club Premium Membership - big benefits and savings

1 KUDOS received
Manager
Manager
User avatar
Joined: 18 Sep 2010
Posts: 53
Followers: 2

Kudos [?]: 24 [1] , given: 303

Re: If line L passes through [#permalink] New post 31 Mar 2011, 07:56
1
This post received
KUDOS
this means that L exactly passes through 2 quadrants.
these quadrants are:1,3 or 2,4
<see picture;>
and L:y=x (for quadrants 1&3)==>slop=1 (positive)
and L:y=-x (for quadrants 2&4)==>slop=-1 (negative)
therfore, the correct answer is C;
Attachments

sq.png
sq.png [ 5.47 KiB | Viewed 1159 times ]

sq.png
sq.png [ 4.98 KiB | Viewed 1157 times ]


_________________

(\ /)
(O.o)
(> <)
This is Bunny. Copy Bunny into your signature to help him on his way to world domination

Re: If line L passes through   [#permalink] 31 Mar 2011, 07:56
    Similar topics Author Replies Last post
Similar
Topics:
2 In a rectangular coordinate system, if a line passes through the point vatsavayi 2 23 Oct 2014, 00:17
13 Experts publish their posts in the topic In the coordinate plane, line k passes through the origin an Bunuel 7 19 Feb 2014, 00:17
4 Experts publish their posts in the topic A line L in the (x,y) coordinate plane passes through the po fozzzy 2 12 Jun 2013, 22:32
16 Experts publish their posts in the topic Given line L, and a parallel line that runs through point 12bhang 9 13 Apr 2013, 04:16
37 Experts publish their posts in the topic ln the coordinate plane, line k passes through the origin GMATD11 14 10 Oct 2011, 07:30
Display posts from previous: Sort by

If line L passes through

  Question banks Downloads My Bookmarks Reviews Important topics  


cron

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®.