It is currently 19 Sep 2017, 13:53

### 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

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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

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

Author Message
TAGS:

### Hide Tags

Intern
Joined: 11 Feb 2012
Posts: 12

Kudos [?]: 73 [1], given: 11

If line L in the xy-coordinate plane has a positive slope, [#permalink]

### Show Tags

07 Nov 2012, 06:55
1
KUDOS
19
This post was
BOOKMARKED
00:00

Difficulty:

95% (hard)

Question Stats:

43% (01:12) correct 57% (01:10) wrong based on 619 sessions

### HideShow timer Statistics

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

Kudos [?]: 73 [1], given: 11

Director
Status: Done with formalities.. and back..
Joined: 15 Sep 2012
Posts: 639

Kudos [?]: 642 [1], given: 23

Location: India
Concentration: Strategy, General Management
Schools: Olin - Wash U - Class of 2015
WE: Information Technology (Computer Software)
Re: If line L in the xy-coordinate plane has a positive slope, [#permalink]

### Show Tags

08 Nov 2012, 02:34
1
KUDOS
1
This post was
BOOKMARKED
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

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

Kudos [?]: 642 [1], given: 23

Intern
Joined: 15 Apr 2010
Posts: 48

Kudos [?]: 31 [1], given: 11

Re: If line L in the xy-coordinate plane has a positive slope, [#permalink]

### Show Tags

08 Nov 2012, 07:31
1
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

Kudos [?]: 31 [1], given: 11

VP
Status: Been a long time guys...
Joined: 03 Feb 2011
Posts: 1381

Kudos [?]: 1632 [3], given: 62

Location: United States (NY)
Concentration: Finance, Marketing
GPA: 3.75
Re: If line L in the xy-coordinate plane has a positive slope, [#permalink]

### Show Tags

08 Nov 2012, 10:57
3
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

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 [ 3.31 KiB | Viewed 18903 times ]

File comment: Diagram 2

fig2.png [ 8.06 KiB | Viewed 18898 times ]

_________________

Kudos [?]: 1632 [3], given: 62

Manager
Joined: 27 Jan 2013
Posts: 71

Kudos [?]: 23 [1], given: 38

Location: India
Concentration: General Management, Operations
GMAT 1: 740 Q50 V40
GPA: 3.51
WE: Other (Transportation)
Re: If line L in the xy-coordinate plane has a positive slope, [#permalink]

### Show Tags

02 Apr 2013, 10:25
1
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??

Kudos [?]: 23 [1], given: 38

Manager
Joined: 11 Jun 2010
Posts: 84

Kudos [?]: 18 [1], given: 17

Re: If line L in the xy-coordinate plane has a positive slope, [#permalink]

### Show Tags

02 Apr 2013, 16:39
1
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 [ 67.78 KiB | Viewed 17327 times ]

Kudos [?]: 18 [1], given: 17

Manager
Joined: 27 Jan 2013
Posts: 71

Kudos [?]: 23 [0], given: 38

Location: India
Concentration: General Management, Operations
GMAT 1: 740 Q50 V40
GPA: 3.51
WE: Other (Transportation)
Re: If line L in the xy-coordinate plane has a positive slope, [#permalink]

### Show Tags

02 Apr 2013, 21:01
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

Kudos [?]: 23 [0], given: 38

Intern
Joined: 28 Jan 2013
Posts: 8

Kudos [?]: 14 [2], given: 4

Location: United States
Concentration: Strategy, Technology
GMAT Date: 04-20-2013
GPA: 3.2
WE: Analyst (Computer Software)
Re: If line L in the xy-coordinate plane has a positive slope, [#permalink]

### Show Tags

03 Apr 2013, 12:41
2
KUDOS
1
This post was
BOOKMARKED
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

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 ?

Kudos [?]: 14 [2], given: 4

Manager
Status: Looking to improve
Joined: 15 Jan 2013
Posts: 174

Kudos [?]: 71 [4], given: 65

GMAT 1: 530 Q43 V20
GMAT 2: 560 Q42 V25
GMAT 3: 650 Q48 V31
Re: If line L in the xy-coordinate plane has a positive slope, [#permalink]

### Show Tags

03 Apr 2013, 13:15
4
KUDOS
1
This post was
BOOKMARKED
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

Kudos [?]: 71 [4], given: 65

Manager
Joined: 27 Jan 2013
Posts: 71

Kudos [?]: 23 [0], given: 38

Location: India
Concentration: General Management, Operations
GMAT 1: 740 Q50 V40
GPA: 3.51
WE: Other (Transportation)
Re: If line L in the xy-coordinate plane has a positive slope, [#permalink]

### Show Tags

03 Apr 2013, 21:29
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

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
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.

Kudos [?]: 23 [0], given: 38

Verbal Forum Moderator
Joined: 10 Oct 2012
Posts: 629

Kudos [?]: 1315 [3], given: 136

Re: If line L in the xy-coordinate plane has a positive slope, [#permalink]

### Show Tags

04 Apr 2013, 10:15
3
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

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.
_________________

Kudos [?]: 1315 [3], given: 136

Director
Status: Verbal Forum Moderator
Joined: 17 Apr 2013
Posts: 612

Kudos [?]: 607 [0], given: 298

Location: India
GMAT 1: 710 Q50 V36
GMAT 2: 750 Q51 V41
GMAT 3: 790 Q51 V49
GPA: 3.3
Re: If line L in the xy-coordinate plane has a positive slope, [#permalink]

### Show Tags

23 Mar 2014, 04:50
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.
My Debrief: http://gmatclub.com/forum/how-to-score-750-and-750-i-moved-from-710-to-189016.html

Kudos [?]: 607 [0], given: 298

Manager
Joined: 03 Dec 2013
Posts: 64

Kudos [?]: 86 [2], given: 35

Re: If line L in the xy-coordinate plane has a positive slope, [#permalink]

### Show Tags

24 Mar 2014, 00:12
2
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.

Hope this helps!

Kudos [?]: 86 [2], given: 35

GMAT Club Legend
Joined: 09 Sep 2013
Posts: 17563

Kudos [?]: 270 [0], given: 0

Re: If line L in the xy-coordinate plane has a positive slope, [#permalink]

### Show Tags

27 Jul 2015, 22:41
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.
_________________

Kudos [?]: 270 [0], given: 0

Manager
Joined: 03 May 2013
Posts: 75

Kudos [?]: 13 [0], given: 105

Re: If line L in the xy-coordinate plane has a positive slope, [#permalink]

### Show Tags

01 Nov 2015, 03:38
i do have couple of questions on this

can we say the if coordinates like a,b and -a-b lie on line the it must passes threw origin ??
what if the line has negative slope and all the conditions are same .

Kudos [?]: 13 [0], given: 105

GMAT Club Legend
Joined: 09 Sep 2013
Posts: 17563

Kudos [?]: 270 [0], given: 0

Re: If line L in the xy-coordinate plane has a positive slope, [#permalink]

### Show Tags

11 Nov 2016, 03:36
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.
_________________

Kudos [?]: 270 [0], given: 0

Intern
Joined: 26 Aug 2015
Posts: 40

Kudos [?]: 24 [0], given: 28

Concentration: Strategy, Economics
GMAT 1: 570 Q40 V28
GMAT 2: 740 Q49 V41
Re: If line L in the xy-coordinate plane has a positive slope, [#permalink]

### Show Tags

17 Nov 2016, 15:51
Hello Bunuel,

could you deliver a clear explanation on why the first statement is sufficient? I see a lot of comments jumping from m=(d-b)/(c-a) to m = d/c. I really don't quite understand how that happens.

Thank you
_________________

Send some kudos this way if I was helpful! !

Kudos [?]: 24 [0], given: 28

Manager
Joined: 22 Feb 2016
Posts: 107

Kudos [?]: 9 [0], given: 208

Location: India
Concentration: Economics, Healthcare
GMAT 1: 690 Q42 V47
GMAT 2: 710 Q47 V39
GPA: 3.57
Re: If line L in the xy-coordinate plane has a positive slope, [#permalink]

### Show Tags

24 Nov 2016, 10:18
1
This post was
BOOKMARKED
This looks like a humugously crazy problem but a little analysis of the concepts will help you reach the solution in 1:15 sec (The time I took )
First lets remove all the flab and look at the core of the question .
y=mx+c
x intercept so y=0 hence x=-c/m

So we need the value of C and the slope of the line.

Statement1- it is given (a,b) and (c,d) and ad=bc
so manipulating the factors a/b=c/d=k . the ratio of all values of x coordinates and y coordinates will be the same only when the line passes throught the origin. x=y (equation of the line) . hence when y=0 then x=0
then Statemnt 1 is sufficient.

This can be proved algebraically too, let a=cb/d. now put the values in the equation of line y-y1=m(x-x1)

Statement 2: We have two point (m,n) and (-m,-n) and they both lie of the line L. Wow what will be the midpoint (0,0). Voila! you got it. The line passes through the origin. What else can you ask for. We have x=0 when y=0.
Sufficienet

Thus D.

Treat yourself with a cupcake now

Kudos [?]: 9 [0], given: 208

VP
Joined: 14 Nov 2016
Posts: 1100

Kudos [?]: 1039 [0], given: 375

Location: Malaysia
Re: If line L in the xy-coordinate plane has a positive slope, [#permalink]

### Show Tags

06 Jun 2017, 00:37
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

Hi Bunuel,

Could you help with this question?
_________________

"Be challenged at EVERY MOMENT."

“Strength doesn’t come from what you can do. It comes from overcoming the things you once thought you couldn’t.”

"Each stage of the journey is crucial to attaining new heights of knowledge."

Kudos [?]: 1039 [0], given: 375

Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 7604

Kudos [?]: 16875 [1], given: 230

Location: Pune, India
Re: If line L in the xy-coordinate plane has a positive slope, [#permalink]

### Show Tags

07 Jun 2017, 21:27
1
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

Responding to a pm:

The equation of a line is
y = mx + c
We are given that m is positive. We need to find the x intercept.

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

So d/c = b/a = y co-ordinate/x co-ordinate

Equation of the line: y/x = m + c/x

So the value of y/x is dependent on the value of x and hence will change for every point on the line.
If the value is the same for two distinct points, it means c = 0. So the equation of the line is
y = mx and it passes through (0, 0) and has x intercept as 0.
Sufficient

(2) There are constants m and n such that the points (m, n) and (–m, –n) are both on line L
Again, since -n/-m = n/m, we have that y/x is same for two distinct points.
So by the same logic as above, this statement is also sufficient alone.

_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Get started with Veritas Prep GMAT On Demand for \$199

Veritas Prep Reviews

Kudos [?]: 16875 [1], given: 230

Re: If line L in the xy-coordinate plane has a positive slope,   [#permalink] 07 Jun 2017, 21:27

Go to page    1   2    Next  [ 21 posts ]

Similar topics Replies Last post
Similar
Topics:
3 If line k in the xy–coordinate plane has slope -3/2, does line k pass 4 16 Oct 2016, 00:59
2 In the xy-plane, if line l has negative slope and passes through the 2 15 Sep 2017, 01:40
2 In the xy-plane, if line l has negative slope and passes 2 17 Sep 2012, 04:52
5 Is the slope of Line L positive? 3 06 May 2017, 06:53
23 In xy-coordinate plane, the slope of line L is 3/4. Does lin 13 31 Jan 2017, 18:42
Display posts from previous: Sort by