Last visit was: 25 Apr 2024, 15:26 It is currently 25 Apr 2024, 15:26
Decision Tracker
My Rewards
New comers' posts
New posts
Unanswered

Close

GRE Prep 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 GRE 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
PREVIOUS TOPIC
NEXT TOPIC

Perpendicular lines m and n intersect at point (a, b),

Tags :
Find Similar Topics  About  Add a Tag

Show Tags
Hide Tags

User avatar
D
Carcass
Verbal Expert
Joined: 18 Apr 2015
Posts: 28635
Own Kudos [?]: 33119 [13]
Given Kudos: 25177
Send PM
Perpendicular lines m and n intersect at point (a, b), [#permalink] New post   06 Aug 2017, 10:27
4
Expert Reply
9
Bookmarks
00:00

Question Stats:

36% (02:16) correct 63% (02:04) wrong based on 128 sessions

Hide Show timer Statistics



Perpendicular lines m and n intersect at point (a, b), where a > b > 0. The slope of line m is between 0 and 1. Which of the following statements MUST be true ?

Indicate all such statements.

❑ The x-intercept of line m is positive.

❑ The y-intercept of line m is negative

❑ The x-intercept of line n is positive.

❑ The y-intercept of line n is negative.

❑ The product of the x- and y-intercepts of line m is not positive,

❑ The sum of the x-intercepts of lines m and n is positive.
ShowHide Answer
Official Answer
C,E
avatar
Avraheem
Intern
Intern
Joined: 14 Jun 2018
Posts: 36
Own Kudos [?]: 13 [0]
Given Kudos: 0
Send PM
Re: Perpendicular lines m and n intersect at point (a, b), [#permalink] New post   27 Jun 2018, 07:13
Hello guys. Why (A) and (F) are not true? How you broach the solution here?
avatar
pranab223
Retired Moderator
Joined: 20 Apr 2016
Posts: 1307
Own Kudos [?]: 2214 [3]
Given Kudos: 251
WE:Engineering (Energy and Utilities)
Send PM

Top Member of the Month
Re: Perpendicular lines m and n intersect at point (a, b), [#permalink] New post   01 Jul 2018, 20:31
2
1
Bookmarks
Avraheem wrote:
Hello guys. Why (A) and (F) are not true? How you broach the solution here?



Hello Avraheem,

I hope you are aware with x- intercept, y- intercept, slope of a line, Positive slop and negative slope

Back to the question:

Here the line m is a positve slop and it lies between 0 and 1 and we know that the slope of one perpendicular line is negative reciprocal of the other

So if slope of m = 1 then the slope of line n = \(-\frac{1}{1}\) =\(-1\)

Option A and Option F: The x intercept may not be always positive. We are given that the slope of the line m is positive and lies between 0 and 1. For this x intercept can be negative, positive or zero, whereas the y intercept always remain positive.

For the line n the x intercept and y intercept will always be positive

As there are are no. of possibility of x-intercept for line m ; so option F is also not correct
avatar
Avraheem
Intern
Intern
Joined: 14 Jun 2018
Posts: 36
Own Kudos [?]: 13 [0]
Given Kudos: 0
Send PM
Re: Perpendicular lines m and n intersect at point (a, b), [#permalink] New post   21 Jul 2018, 23:16
pranab01 wrote:
Avraheem wrote:
Hello guys. Why (A) and (F) are not true? How you broach the solution here?



Hello Avraheem,

I hope you are aware with x- intercept, y- intercept, slope of a line, Positive slop and negative slope

Back to the question:

Here the line m is a positve slop and it lies between 0 and 1 and we know that the slope of one perpendicular line is negative reciprocal of the other

So if slope of m = 1 then the slope of line n = \(-\frac{1}{1}\) =\(-1\)

Option A and Option F: The x intercept may not be always positive. We are given that the slope of the line m is positive and lies between 0 and 1. For this x intercept can be negative, positive or zero, whereas the y intercept always remain positive.

For the line n the x intercept and y intercept will always be positive

As there are are no. of possibility of x-intercept for line m ; so option F is also not correct


Thanks a lot. Last question, why line m can not pass through (0,0), which is neither positive nor negative?
avatar
ShubhiNigam29
Intern
Intern
Joined: 21 Jun 2018
Posts: 35
Own Kudos [?]: 14 [0]
Given Kudos: 0
Send PM
Re: Perpendicular lines m and n intersect at point (a, b), [#permalink] New post   05 Aug 2018, 04:26
Carcass wrote:

This question is part of GREPrepClub - The Questions Vault Project



Perpendicular lines m and n intersect at point (a, b), where a > b > 0. The slope of line m is between 0 and 1. Which of the following statements MUST be true ?

Indicate all such statements.

❑ The x-intercept of line m is positive.

❑ The y-intercept of line m is negative

❑ The x-intercept of line n is positive.

❑ The y-intercept of line n is negative.

❑ The product of the x- and y-intercepts of line m is not positive,

❑ The sum of the x-intercepts of lines m and n is positive.

Show: :: OA
C,E


Please explain why A & F are not correct?
avatar
AE
Director
Director
Joined: 09 Nov 2018
Posts: 505
Own Kudos [?]: 129 [0]
Given Kudos: 0
Send PM
Re: Perpendicular lines m and n intersect at point (a, b), [#permalink] New post   05 Jan 2019, 17:15
Avraheem wrote:

Thanks a lot. Last question, why line m can not pass through (0,0), which is neither positive nor negative?


Because the slope is between 0-1
avatar
AE
Director
Director
Joined: 09 Nov 2018
Posts: 505
Own Kudos [?]: 129 [0]
Given Kudos: 0
Send PM
Re: Perpendicular lines m and n intersect at point (a, b), [#permalink] New post   05 Jan 2019, 17:17
ShubhiNigam29 wrote:

Please explain why A & F are not correct?


Check this

pranab01 wrote:

Option A and Option F: The x intercept may not be always positive. We are given that the slope of the line m is positive and lies between 0 and 1. For this x intercept can be negative, positive or zero, whereas the y intercept always remain positive.

For the line n the x intercept and y intercept will always be positive

As there are are no. of possibility of x-intercept for line m ; so option F is also not correct
avatar
chetan2u
Supreme Moderator
Joined: 01 Nov 2017
Posts: 371
Own Kudos [?]: 442 [3]
Given Kudos: 0
Send PM
Re: Perpendicular lines m and n intersect at point (a, b), [#permalink] New post   05 Jan 2019, 20:36
2
Expert Reply
1
Bookmarks
Carcass wrote:

This question is part of GREPrepClub - The Questions Vault Project



Perpendicular lines m and n intersect at point (a, b), where a > b > 0. The slope of line m is between 0 and 1. Which of the following statements MUST be true ?

Indicate all such statements.

❑ The x-intercept of line m is positive.

❑ The y-intercept of line m is negative

❑ The x-intercept of line n is positive.

❑ The y-intercept of line n is negative.

❑ The product of the x- and y-intercepts of line m is not positive,

❑ The sum of the x-intercepts of lines m and n is positive.


You can draw a sketch to be more clear on the regions these lines can be formed
Look at the attached figure..
(I) The red line is where a=b but a>b>0, so the point will lie below this line...
(II) A point (a,b) is taken and the light grey colour is the portion wher line m can exist passing through (a,b) and GREEN portion is wher line n can exist.

Line m - As we can see it can have x intercept and y-intercept both negative and positive, so eliminate A, B and F..
Line n - We can see that the x intercept and y-intercept both will be positive.. So, C and E are true and eliminate D

ans C and E
Attachments

00000.png
00000.png [ 33.32 KiB | Viewed 9294 times ]

avatar
ashhadbgmail
Intern
Intern
Joined: 18 Mar 2023
Posts: 1
Own Kudos [?]: 0 [0]
Given Kudos: 0
Send PM
Re: Perpendicular lines m and n intersect at point (a, b), [#permalink] New post   20 Mar 2023, 02:46
❑ The product of the x- and y-intercepts of line m is not positive,

this line can pass through the origin also
if you shift the line without changing its slope, it can be seen that it can pass through
the origin and thus
the product can be zero, i.e neither positive nor negative

plz comment
avatar
B
emmar
Intern
Intern
Joined: 26 Dec 2023
Posts: 44
Own Kudos [?]: 14 [0]
Given Kudos: 4
Send PM
Re: Perpendicular lines m and n intersect at point (a, b), [#permalink] New post   28 Dec 2023, 12:33
ashhadbgmail wrote:
❑ The product of the x- and y-intercepts of line m is not positive,

this line can pass through the origin also
if you shift the line without changing its slope, it can be seen that it can pass through
the origin and thus
the product can be zero, i.e neither positive nor negative

plz comment


Are you asking a question? Because you're right. Product can be zero, or it can be negative. But not positive.
Prep Club for GRE Bot
gmatclubot
[#permalink]
Moderators:
BrushMyQuant
Moderator
1085 posts
VibhuAnurag
GRE Instructor
218 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Main navigation

Partners

GRE Resources

www.ets.org/gre | About | Terms and Conditions and Privacy Policy | Prep Club for GRE Rules | Contact