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

It is currently 21 Aug 2014, 06:45

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 in the xy-coordinate plane has a positive slope,

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
1 KUDOS received
Intern
Intern
avatar
Joined: 11 Feb 2012
Posts: 12
Followers: 0

Kudos [?]: 5 [1] , given: 11

GMAT Tests User
If line L in the xy-coordinate plane has a positive slope, [#permalink] New post 07 Nov 2012, 05:55
1
This post received
KUDOS
4
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

44% (02:05) correct 56% (01:04) wrong based on 183 sessions
If line L in the xy-coordinate plane has a positive slope, what is the x-intercept of L ?

(1) There are different points (a, b) and (c, d) on line L such that ad = bc.

(2) There are constants m and n such that the points (m, n) and (–m, –n) are both on line L
[Reveal] Spoiler: OA
Expert Post
3 KUDOS received
Verbal Forum Moderator
Verbal Forum Moderator
User avatar
Status: Preparing for the another shot...!
Joined: 03 Feb 2011
Posts: 1425
Location: India
Concentration: Finance, Marketing
GPA: 3.75
Followers: 127

Kudos [?]: 590 [3] , given: 62

GMAT ToolKit User GMAT Tests User Premium Member
Re: If line L in the xy-coordinate plane has a positive slope, [#permalink] New post 08 Nov 2012, 09:57
3
This post received
KUDOS
Expert's post
smartass666 wrote:
If line L in the xy-coordinate plane has a positive slope, what is the x-intercept of L ?

(1) There are different points (a, b) and (c, d) on line L such that ad = bc.

(2) There are constants m and n such that the points (m, n) and (–m, –n) are both on line L


Given fact: Line L has a positive slope.

Statement 1) ad=bc, where(a,b) is different from (b,c)
Now if you see the diagram, you will observe that the product of two "outer" values is greater than the product of two "inner"values.
The first diagram clearly depicts a line passing through quadrants III, II and I , and is also a representative of other such lines. If you clearly see, the product of and d will only be equal to the product of b and c, only when they are either sides of origin and opposite to each other. (as shown in the other diagram)

Statement 2) states the same in other words.

Hence D
Attachments

File comment: Diagram 1
fig1.png
fig1.png [ 3.31 KiB | Viewed 6335 times ]

File comment: Diagram 2
fig2.png
fig2.png [ 8.06 KiB | Viewed 6336 times ]


_________________

Prepositional Phrases Clarified|Elimination of BEING| Absolute Phrases Clarified
Rules For Posting
www.Univ-Scholarships.com

2 KUDOS received
Manager
Manager
avatar
Status: Looking to improve
Joined: 15 Jan 2013
Posts: 177
GMAT 1: 530 Q43 V20
GMAT 2: 560 Q42 V25
GMAT 3: 650 Q48 V31
Followers: 1

Kudos [?]: 36 [2] , given: 65

Re: If line L in the xy-coordinate plane has a positive slope, [#permalink] New post 03 Apr 2013, 12:15
2
This post received
KUDOS
Dipankar,

To understand why stmt 1 is sufficient, let's revisit a line equation. A line is represented using y = mx +k in which m is the slope and k is the y-intercept.

Taking stmt 1, the m = d-b/c-a = d/c. Hence y = (d/c )x + k and to find k just use one of the points on the line. Using point (c, d) in the line y= (d/c)x + k gives k = 0. hence the equation of the line passing through points (a,b) and (c,d) is y = (d/c)x and to find x intercept set y = 0, which will result in x = 0.

Hope this is clear..

//kudos please, if this explanation helps you
_________________

KUDOS is a way to say Thank You

Expert Post
2 KUDOS received
Verbal Forum Moderator
Verbal Forum Moderator
User avatar
Joined: 10 Oct 2012
Posts: 627
Followers: 41

Kudos [?]: 550 [2] , given: 135

Premium Member
Re: If line L in the xy-coordinate plane has a positive slope, [#permalink] New post 04 Apr 2013, 09:15
2
This post received
KUDOS
Expert's post
smartass666 wrote:
If line L in the xy-coordinate plane has a positive slope, what is the x-intercept of L ?

(1) There are different points (a, b) and (c, d) on line L such that ad = bc.

(2) There are constants m and n such that the points (m, n) and (–m, –n) are both on line L


From F.S 1, we have that the slope of the given line is (d-b)/(c-a). Again, we have d = (bc)/a ; the slope is = b/a. Now in the equation, y = mx+c, just plugin the value of m = b/a and the point (a,b)--> we get c= 0, thus the line passes through the origin. The x intercept is 0.Sufficient.

From F.S 2, we have that both the points (m,n) and (-m,-n) lie on the same line.Thus, we can see that the mid-point of these 2 points is at the origin. Line passes through the origin, hence the x-intercept = 0. Sufficient.

D.
_________________

All that is equal and not-Deep Dive In-equality

Hit and Trial for Integral Solutions

1 KUDOS received
Director
Director
User avatar
Status: Done with formalities.. and back..
Joined: 15 Sep 2012
Posts: 646
Location: India
Concentration: Strategy, General Management
Schools: Olin - Wash U - Class of 2015
WE: Information Technology (Computer Software)
Followers: 35

Kudos [?]: 353 [1] , given: 23

GMAT ToolKit User Premium Member
Re: If line L in the xy-coordinate plane has a positive slope, [#permalink] New post 08 Nov 2012, 01:34
1
This post received
KUDOS
smartass666 wrote:
If line L in the xy-coordinate plane has a positive slope, what is the x-intercept of L ?

(1) There are different points (a, b) and (c, d) on line L such that ad = bc.
(2) There are constants m and n such that the points (m, n) and (–m, –n) are both on line L


Statement 1: ad =bc =>
b/a = d/c = m (assume)
Each point lies on a line which passes through origin. (y=mx+c and c=0 making it y=mx)

So x intercept =0 . Sufficient

Statement 2: (m,n) and (-m,-n) on same line. m and -m are mirror image across Y axis. n and -n are mirror image across x axis. thus (m,n) and (-m,-n) are mirror image of each other across origin. Thus a line joining these points must go through origin.

So x intercept =0 . Sufficient

Hence ans D it is.
_________________

Lets Kudos!!! ;-)
Black Friday Debrief

1 KUDOS received
Intern
Intern
avatar
Joined: 15 Apr 2010
Posts: 48
Followers: 0

Kudos [?]: 16 [1] , given: 10

Re: If line L in the xy-coordinate plane has a positive slope, [#permalink] New post 08 Nov 2012, 06:31
1
This post received
KUDOS
(1): a/b = c/d --> 2 points pass through the same slope. Note that k slope = y/x (y advances a units for for every unit x advances) --> line passes through 0 (y=kx) --> suff
(2) (m,n) and (-m, -n) belong to (l) --> they are opposite of each other through the origin O --> suff

--> D
1 KUDOS received
Manager
Manager
avatar
Joined: 27 Jan 2013
Posts: 58
Location: India
Concentration: Social Entrepreneurship, Operations
Schools: ISB '15
GMAT 1: 740 Q50 V40
GPA: 3.51
WE: Other (Transportation)
Followers: 2

Kudos [?]: 18 [1] , given: 33

Re: If line L in the xy-coordinate plane has a positive slope, [#permalink] New post 02 Apr 2013, 09:25
1
This post received
KUDOS
catennacio wrote:
(1): a/b = c/d --> 2 points pass through the same slope. Note that k slope = y/x (y advances a units for for every unit x advances) --> line passes through 0 (y=kx) --> suff
(2) (m,n) and (-m, -n) belong to (l) --> they are opposite of each other through the origin O --> suff

--> D


(1): a/b = c/d --> 2 points pass through the same slope. Note that k slope = y/x (y advances a units for for every unit x advances) --> line passes through 0 (y=kx) --> suff

Can some mathwiz clarify a little more on this.
I do not understand how if a/b = c/d the line passes through the origin??
1 KUDOS received
Manager
Manager
avatar
Joined: 11 Jun 2010
Posts: 84
Followers: 0

Kudos [?]: 7 [1] , given: 17

Re: If line L in the xy-coordinate plane has a positive slope, [#permalink] New post 02 Apr 2013, 15:39
1
This post received
KUDOS
ST 1: ad = cb for any 2 combination of points (a,b) and (c,d) that fulfils the equation ad = bc will pass through origin (as shown in attached graph)
hence SUFFICIENT (as x intercept = 0)

St 2: (m,n) and (-m, -n) lie on the line. Any combination of points on a line that satisfy this equation will pass through origin
hence SUFFICIENT (as x intercept = 0)

Ans is D
Attachments

ab=cd graph.JPG
ab=cd graph.JPG [ 67.78 KiB | Viewed 4768 times ]

1 KUDOS received
Intern
Intern
avatar
Joined: 28 Jan 2013
Posts: 8
Location: United States
Concentration: Strategy, Technology
GMAT Date: 04-20-2013
GPA: 3.2
WE: Analyst (Computer Software)
Followers: 0

Kudos [?]: 8 [1] , given: 4

Re: If line L in the xy-coordinate plane has a positive slope, [#permalink] New post 03 Apr 2013, 11:41
1
This post received
KUDOS
Dipankar6435 wrote:
srcc25anu wrote:
ST 1: ad = cb for any 2 combination of points (a,b) and (c,d) that fulfils the equation ad = bc will pass through origin (as shown in attached graph)
hence SUFFICIENT (as x intercept = 0)

St 2: (m,n) and (-m, -n) lie on the line. Any combination of points on a line that satisfy this equation will pass through origin
hence SUFFICIENT (as x intercept = 0)

Ans is D


With the risk of sounding especially dumb i wish to resubmit my doubts regarding this
St 2 does make sense to me (m,n) and (-m,-n) are mirror images of each other about the origin. Thus they must lie on line y = x . GOT IT
St 1 still unclear
srcc25anu your graph is pretty neat but i just cannot comprehend how knowing that the product of x and y coordinates being equal (i.e x1*y1 = x2*y2) makes the line containing them pass though the origin
Can i get a link to some articles where such nuances of coordinate geometry are explained in detail
Apologies for being such a pain :oops:


Just to keep you correct on ST2. The Line is Y=KX not Y=X. The slope may or may not be 1.

In case of ST2.

Slope of any line = (Y2 - Y1)/X2- X1
if point (X1,Y1) is origin then slope = Y2/X2

Similary, for any other point (X3,Y3) on same line

Slope = Y3/X3

Y3/X3 = Y2/X2
X2 * Y3 = Y2 * X3 ( This holds true for all lines passing through origin)

for points (a,b) & (c,d)

a * d = b * c ( This is what was given in question. )

Does this help ?
1 KUDOS received
Manager
Manager
avatar
Joined: 03 Dec 2013
Posts: 57
Followers: 0

Kudos [?]: 14 [1] , given: 27

Re: If line L in the xy-coordinate plane has a positive slope, [#permalink] New post 23 Mar 2014, 23:12
1
This post received
KUDOS
Hi Honchos,
Let me try to explain:
as you know eqn of line is y = mx + e (e is y intercept)

St1: Points (a,b) and (c,d) lies on above line.
So
b = ma + e ..(i)
d = mc + e ..(ii)
dividing (i) by (ii) we get
b/d = (ma + e) / (mc + e).
Also we know ad = bc. Thus b/d = a/c. Substituting in above we get:
a/c = (ma + e) / (mc + e)
(mac + ea) = (mac + ec)
solving above, ea - ec = 0 --> e(a-c) = 0, from this we can say that either e = 0 or a = c. But a cannot be equal to c (as they are two different points). So e = 0.
Final eqn; y = mx .. which indicates that line passes through origin. So x intercept = 0.

Sufficient.

st2: since (m,n) & (-m,-n) are two end points of segment passing through origin, and line l also contains this points, we can say that line l passes through origin. So x intercept = 0.
Sufficient.

Answer: D

Hope this helps!
Manager
Manager
avatar
Joined: 27 Jan 2013
Posts: 58
Location: India
Concentration: Social Entrepreneurship, Operations
Schools: ISB '15
GMAT 1: 740 Q50 V40
GPA: 3.51
WE: Other (Transportation)
Followers: 2

Kudos [?]: 18 [0], given: 33

Re: If line L in the xy-coordinate plane has a positive slope, [#permalink] New post 02 Apr 2013, 20:01
srcc25anu wrote:
ST 1: ad = cb for any 2 combination of points (a,b) and (c,d) that fulfils the equation ad = bc will pass through origin (as shown in attached graph)
hence SUFFICIENT (as x intercept = 0)

St 2: (m,n) and (-m, -n) lie on the line. Any combination of points on a line that satisfy this equation will pass through origin
hence SUFFICIENT (as x intercept = 0)

Ans is D


With the risk of sounding especially dumb i wish to resubmit my doubts regarding this
St 2 does make sense to me (m,n) and (-m,-n) are mirror images of each other about the origin. Thus they must lie on line y = x . GOT IT
St 1 still unclear
srcc25anu your graph is pretty neat but i just cannot comprehend how knowing that the product of x and y coordinates being equal (i.e x1*y1 = x2*y2) makes the line containing them pass though the origin
Can i get a link to some articles where such nuances of coordinate geometry are explained in detail
Apologies for being such a pain :oops:
Manager
Manager
avatar
Joined: 27 Jan 2013
Posts: 58
Location: India
Concentration: Social Entrepreneurship, Operations
Schools: ISB '15
GMAT 1: 740 Q50 V40
GPA: 3.51
WE: Other (Transportation)
Followers: 2

Kudos [?]: 18 [0], given: 33

Re: If line L in the xy-coordinate plane has a positive slope, [#permalink] New post 03 Apr 2013, 20:29
hikaps14 wrote:
Dipankar6435 wrote:
srcc25anu wrote:
ST 1: ad = cb for any 2 combination of points (a,b) and (c,d) that fulfils the equation ad = bc will pass through origin (as shown in attached graph)
hence SUFFICIENT (as x intercept = 0)

St 2: (m,n) and (-m, -n) lie on the line. Any combination of points on a line that satisfy this equation will pass through origin
hence SUFFICIENT (as x intercept = 0)

Ans is D


With the risk of sounding especially dumb i wish to resubmit my doubts regarding this
St 2 does make sense to me (m,n) and (-m,-n) are mirror images of each other about the origin. Thus they must lie on line y = x . GOT IT
St 1 still unclear
srcc25anu your graph is pretty neat but i just cannot comprehend how knowing that the product of x and y coordinates being equal (i.e x1*y1 = x2*y2) makes the line containing them pass though the origin
Can i get a link to some articles where such nuances of coordinate geometry are explained in detail
Apologies for being such a pain :oops:


Just to keep you correct on ST2. The Line is Y=KX not Y=X. The slope may or may not be 1.

In case of ST2.

Slope of any line = (Y2 - Y1)/X2- X1
if point (X1,Y1) is origin then slope = Y2/X2

Similary, for any other point (X3,Y3) on same line

Slope = Y3/X3

Y3/X3 = Y2/X2
X2 * Y3 = Y2 * X3 ( This holds true for all lines passing through origin)

for points (a,b) & (c,d)

a * d = b * c ( This is what was given in question. )

Does this help ?


It helps greatly. Thanks :-D
So I can add this to my cheat sheet now-
If y1/x1 = y2/x2 then the line containing the points (x1,y1) and (x2,y2) passes through the origin. :idea:
Director
Director
avatar
Joined: 17 Apr 2013
Posts: 511
Concentration: Entrepreneurship, Leadership
Schools: HBS '16
GMAT Date: 11-30-2013
GPA: 3.3
Followers: 2

Kudos [?]: 23 [0], given: 238

CAT Tests
Re: If line L in the xy-coordinate plane has a positive slope, [#permalink] New post 23 Mar 2014, 03:50
Bunuel,

I am unable to Convince Myself why this option is also correct-

"(1) There are different points (a, b) and (c, d) on line L such that ad = bc."
_________________

Like my post Send me a Kudos :) It is a Good manner.

Manager
Manager
avatar
Joined: 17 Jul 2013
Posts: 101
Followers: 0

Kudos [?]: 1 [0], given: 65

Re: If line L in the xy-coordinate plane has a positive slope, [#permalink] New post 01 Jul 2014, 11:27
Hi Bunuel,

Can you please help me to understand this one ...
Re: If line L in the xy-coordinate plane has a positive slope,   [#permalink] 01 Jul 2014, 11:27
    Similar topics Author Replies Last post
Similar
Topics:
5 Experts publish their posts in the topic In xy-coordinate plane, the slope of line L is 3/4. Does lin kabilank87 7 23 Apr 2013, 00:07
2 In the xy-plane, if line l has negative slope and passes crackmba2012 2 17 Sep 2012, 02:14
15 Experts publish their posts in the topic In the xy plane line k has a positive slope and and cmugeria 14 09 Sep 2010, 09:08
In the xy-coordinate plane, line L and K intersect at the jimjohn 1 26 Dec 2007, 19:03
In an xy plane, line k has a positive slope and x-intercept jlui4477 1 26 Feb 2006, 21:58
Display posts from previous: Sort by

If line L in the xy-coordinate plane has a positive slope,

  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®.