 It is currently 16 Jun 2019, 22:45 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. Perpendicular lines m and n intersect at point (a, b),  Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS: Founder  Joined: 18 Apr 2015
Posts: 6874
Followers: 114

Kudos [?]: 1332  , given: 6293

Perpendicular lines m and n intersect at point (a, b), [#permalink]
2
KUDOS
Expert's post 00:00

Question Stats: 23% (01:13) correct 76% (01:56) wrong based on 34 sessions

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.
[Reveal] Spoiler: OA

_________________
Intern Joined: 14 Jun 2018
Posts: 36
Followers: 0

Kudos [?]: 7 , given: 100

Re: Perpendicular lines m and n intersect at point (a, b), [#permalink]
Hello guys. Why (A) and (F) are not true? How you broach the solution here? Director Joined: 20 Apr 2016
Posts: 901
WE: Engineering (Energy and Utilities)
Followers: 11

Kudos [?]: 666  , given: 147

Re: Perpendicular lines m and n intersect at point (a, b), [#permalink]
2
KUDOS
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
_________________

If you found this post useful, please let me know by pressing the Kudos Button

Rules for Posting https://greprepclub.com/forum/rules-for ... -1083.html

Intern Joined: 14 Jun 2018
Posts: 36
Followers: 0

Kudos [?]: 7 , given: 100

Re: Perpendicular lines m and n intersect at point (a, b), [#permalink]
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?
Intern Joined: 21 Jun 2018
Posts: 35
Followers: 0

Kudos [?]: 6 , given: 11

Re: Perpendicular lines m and n intersect at point (a, b), [#permalink]
Carcass wrote:

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.

[Reveal] Spoiler: OA
C,E

Please explain why A & F are not correct?
Director Joined: 09 Nov 2018
Posts: 508
Followers: 0

Kudos [?]: 27 , given: 1

Re: Perpendicular lines m and n intersect at point (a, b), [#permalink]
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
Director Joined: 09 Nov 2018
Posts: 508
Followers: 0

Kudos [?]: 27 , given: 1

Re: Perpendicular lines m and n intersect at point (a, b), [#permalink]
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
Supreme Moderator
Joined: 01 Nov 2017
Posts: 370
Followers: 5

Kudos [?]: 111 , given: 4

Re: Perpendicular lines m and n intersect at point (a, b), [#permalink]
Expert's post
Carcass wrote:

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 [ 33.32 KiB | Viewed 824 times ]

_________________

Some useful Theory.
1. Arithmetic and Geometric progressions : https://greprepclub.com/forum/progressions-arithmetic-geometric-and-harmonic-11574.html#p27048
2. Effect of Arithmetic Operations on fraction : https://greprepclub.com/forum/effects-of-arithmetic-operations-on-fractions-11573.html?sid=d570445335a783891cd4d48a17db9825
3. Remainders : https://greprepclub.com/forum/remainders-what-you-should-know-11524.html
4. Number properties : https://greprepclub.com/forum/number-property-all-you-require-11518.html
5. Absolute Modulus and Inequalities : https://greprepclub.com/forum/absolute-modulus-a-better-understanding-11281.html Re: Perpendicular lines m and n intersect at point (a, b),   [#permalink] 05 Jan 2019, 20:36
Display posts from previous: Sort by

Perpendicular lines m and n intersect at point (a, b),  Question banks Downloads My Bookmarks Reviews Important topics  Powered by phpBB © phpBB Group Kindly note that the GRE® test is a registered trademark of the Educational Testing Service®, and this site has neither been reviewed nor endorsed by ETS®.