Last visit was: 19 Jul 2024, 23:52 It is currently 19 Jul 2024, 23:52
Toolkit
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
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

# Line D passes through point (-2,5), and the product of its x-intercept

SORT BY:
Tags:
Show Tags
Hide Tags
Intern
Joined: 10 Apr 2011
Posts: 30
Own Kudos [?]: 323 [24]
Given Kudos: 7
Senior Manager
Joined: 03 Feb 2011
Status:Impossible is not a fact. It's an opinion. It's a dare. Impossible is nothing.
Affiliations: University of Chicago Booth School of Business
Posts: 469
Own Kudos [?]: 904 [8]
Given Kudos: 123
Retired Moderator
Joined: 02 Sep 2010
Posts: 613
Own Kudos [?]: 2965 [8]
Given Kudos: 25
Location: London
Q51  V41
General Discussion
Retired Moderator
Joined: 16 Nov 2010
Posts: 903
Own Kudos [?]: 1194 [0]
Given Kudos: 43
Location: United States (IN)
Concentration: Strategy, Technology
Re: Line D passes through point (-2,5), and the product of its x-intercept [#permalink]
The slope of the line is -ve, the only point that makes the slope -ve is D.

(5 - 2)/(-2 + 1) = 3/-1

Tutor
Joined: 16 Oct 2010
Posts: 15125
Own Kudos [?]: 66741 [7]
Given Kudos: 436
Location: Pune, India
Re: Line D passes through point (-2,5), and the product of its x-intercept [#permalink]
2
Kudos
5
Bookmarks
yvonne0923 wrote:
Line D passes through point (-2,5), and the product of its x-intercept and y-intercept is positive. Which of the following points could be on line D?

A. (5,10)
B. (-3,2)
C. (-1,7)
D. (-1,2)
E. (-3,1)
_______________________________________________________________________________________________

Anyone can clarify the meaning of "the product of its x-intercept and y-intercept is positive" on the diagram for me?

Thanks

First and foremost, make sure you draw quick diagrams in coordinate geometry problems. Half your problem will be solved there and then.
So the line would look something like one of these lines if it passes through (-2, 5).

Attachment:

Ques2.jpg [ 11.85 KiB | Viewed 12762 times ]

Further, x-intercept is the point on the x axis where the line intersects the x axis. y intercept is the point on the y axis where the line intersects the y axis. Say if a line passes through (1, 0), its x intercept much be 1. If a line passes through (0, -3), its y intercept must be -3. Of course, for any straight line, x and y intercepts have unique values.

What is the point of giving that the product of x and y intercepts is positive? This implies that either both x and y intercept are positive or both are negative. Now look at the lines above. Would it look something like the green line or the red line?
The red line has negative x intercept and positive y intercept so the product of its intercepts will be -ve. Hence, it cannot be the required line.
The green line has both intercepts positive so it can be our line ( it is downward sloping from left to right hence it has negative slope)
Now, I have plotted the approximate position of all the points. Which one can possibly lie on this line?
Attachment:

Ques3.jpg [ 10.06 KiB | Viewed 12663 times ]

I think it is quite clear that the line can only pass through (-1, 2) and still maintain the negative slope. In all other cases, the line would have a positive slope i.e. it will look like the red line
Manager
Joined: 02 May 2012
Posts: 59
Own Kudos [?]: 692 [0]
Given Kudos: 114
Line D passes through point (-2,5), and the product of its x-intercept [#permalink]
Line D passes through point (-2,5), and the product of its x-intercept and y-intercept is positive. Which of the following points could be on line D?

(A) (5,10)
(B) (-3,2)
(C) (-1,7)
(D) (-1,2)
(E) (-3,1)
Intern
Joined: 20 Jun 2014
Posts: 11
Own Kudos [?]: 16 [2]
Given Kudos: 2
GPA: 3.62
WE:Information Technology (Computer Hardware)
Re: Line D passes through point (-2,5), and the product of its x-intercept [#permalink]
1
Kudos
1
Bookmarks
Here is how i approached the question:
Equation of a line is (y-y1)/(x-x1)=m
y1= 5 , x1 = -2

(y-5)/(x+2)=m
y-5=mx+2m
y=m(x+2)+5

If both the x-intercept and y-intercept are positive, if you draw the line then the slope of the line would be -ve.

Plug in the solutions y=m(x+2)+5, only D will give you a -ve value for m, thus it's the solution , thanks !
Math Expert
Joined: 02 Sep 2009
Posts: 94421
Own Kudos [?]: 642418 [0]
Given Kudos: 86332
Re: Line D passes through point (-2,5), and the product of its x-intercept [#permalink]
aashu4uiit wrote:
Line D passes through point (-2,5), and the product of its x-intercept and y-intercept is positive. Which of the following points could be on line D?

(A) (5,10)
(B) (-3,2)
(C) (-1,7)
(D) (-1,2)
(E) (-3,1)

Merging similar topics. Please refer to the discussion above.
Manager
Joined: 14 Jun 2016
Posts: 112
Own Kudos [?]: 205 [0]
Given Kudos: 54
Location: India
GMAT 1: 610 Q49 V24
GMAT 2: 690 Q49 V33
WE:Engineering (Manufacturing)
Re: Line D passes through point (-2,5), and the product of its x-intercept [#permalink]
VeritasPrepKarishma wrote:
yvonne0923 wrote:
Line D passes through point (-2,5), and the product of its x-intercept and y-intercept is positive. Which of the following points could be on line D?

A. (5,10)
B. (-3,2)
C. (-1,7)
D. (-1,2)
E. (-3,1)
_______________________________________________________________________________________________

Anyone can clarify the meaning of "the product of its x-intercept and y-intercept is positive" on the diagram for me?

Thanks

First and foremost, make sure you draw quick diagrams in coordinate geometry problems. Half your problem will be solved there and then.
So the line would look something like one of these lines if it passes through (-2, 5).

Attachment:
Ques2.jpg

Further, x-intercept is the point on the x axis where the line intersects the x axis. y intercept is the point on the y axis where the line intersects the y axis. Say if a line passes through (1, 0), its x intercept much be 1. If a line passes through (0, -3), its y intercept must be -3. Of course, for any straight line, x and y intercepts have unique values.

What is the point of giving that the product of x and y intercepts is positive? This implies that either both x and y intercept are positive or both are negative. Now look at the lines above. Would it look something like the green line or the red line?
The red line has negative x intercept and positive y intercept so the product of its intercepts will be -ve. Hence, it cannot be the required line.
The green line has both intercepts positive so it can be our line ( it is downward sloping from left to right hence it has negative slope)
Now, I have plotted the approximate position of all the points. Which one can possibly lie on this line?
Attachment:
Ques3.jpg

I think it is quite clear that the line can only pass through (-1, 2) and still maintain the negative slope. In all other cases, the line would have a positive slope i.e. it will look like the red line

Thanks for the excellent explanation; Can you please update new question checking similar concept?
Manager
Joined: 09 Jun 2014
Posts: 225
Own Kudos [?]: 284 [0]
Given Kudos: 205
Location: India
Concentration: General Management, Operations
Re: Line D passes through point (-2,5), and the product of its x-intercept [#permalink]
yvonne0923 wrote:
Line D passes through point (-2,5), and the product of its x-intercept and y-intercept is positive. Which of the following points could be on line D?

A. (5,10)
B. (-3,2)
C. (-1,7)
D. (-1,2)
E. (-3,1)

______________________________________________________________________________________________

Anyone can clarify the meaning of "the product of its x-intercept and y-intercept is positive" on the diagram for me?

Thanks

Since prod of X and Y intercept is postive so line passes through 1st quad or 3rd quad means slope will be negative/Now find M< 0 ..by chosing one point from option and one point as (-2,5)
Non-Human User
Joined: 09 Sep 2013
Posts: 34041
Own Kudos [?]: 853 [0]
Given Kudos: 0
Re: Line D passes through point (-2,5), and the product of its x-intercept [#permalink]
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.
Re: Line D passes through point (-2,5), and the product of its x-intercept [#permalink]
Moderator:
Math Expert
94421 posts