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# Point (r,s) lies on the line L. Is the line s intercept with

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Point (r,s) lies on the line L. Is the line s intercept with [#permalink]

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20 May 2010, 00:54
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65% (hard)

Question Stats:

56% (02:25) correct 44% (01:20) wrong based on 252 sessions

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Point (r,s) lies on the line L. Is the line’s intercept with axis-x greater than r?

(1) L has a negative slope.
(2) s<0
[Reveal] Spoiler: OA

Last edited by Bunuel on 19 Oct 2012, 03:31, edited 1 time in total.
Edited the question.
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Re: Is the line’s intercept with axis-x greater than r? [#permalink]

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20 May 2010, 01:27
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dimitri92 wrote:
Point (r,s) lies on the line L. Is the line’s intercept with axis-x greater than r?
1). L has a negative slope.
2). s<0

Equation of a line in point intercept form is $$y=mx+b$$, where: $$m$$ is the slope of the line; $$b$$ is the y-intercept of the line (the value of $$y$$ for $$x=0$$); $$x$$ is the independent variable of the function $$y$$.

Point (r,s) lies on the line L --> $$s=mr+b$$.

Lines intercept with x-axis (x-intercept) is the value of $$x$$ for $$y=0$$ --> $$x=-\frac{b}{m}$$.

Q: is $$-\frac{b}{m}>r$$? --> substitute $$b$$ and simplify --> $$-\frac{s-mr}{m}>r$$? --> $$-\frac{s}{m}+r>r$$? --> $$\frac{s}{m}<0$$?

So the question became: is $$\frac{s}{m}<0$$? we need to know signs of $$s$$ and $$m$$.

(1) $$m<0$$. No info about $$s$$. Not sufficient.

(2) $$s<0$$. No info about $$m$$. Not sufficient.

(1)+(2) Sufficient.

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Re: Is the line’s intercept with axis-x greater than r? [#permalink]

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01 Nov 2010, 05:16
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This question can be easily solved if you understand the concept of slope and x intercept.

Negative slope means that the line is going down from left to right.
x intercept is the point at which the line crosses the x axis.

You know that (r, s) lies on the line and want to find if x intercept is greater than r.
Statement 1: If line has negative slope, (r, s) could still be above x axis or below x axis on the line. If it is above x axis, r < x intercept. If it is below x axis, r > x intercept. See the 1st diagram below.
Statement 2: If s < 0, it means the point (r, s) lies below x axis (s is the y co-ordinate and it is negative below x axis). But if the slope of the line is positive, r < x intercept and if the slope is negative, r > x intercept. See the 2nd diagram below.
Attachment:

Ques.jpg [ 17.47 KiB | Viewed 3915 times ]

When both the statements are combined, slope of line is negative and (r, s) lies below the x axis, then (r, s) has to lie to the right of the x intercept. Hence r will always be greater than x intercept.
Attachment:

Ques1.jpg [ 9.6 KiB | Viewed 3911 times ]

So we can conclusively answer the question with 'No. Line's x intercept is not greater than r.' Answer (C).
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Re: Is the line’s intercept with axis-x greater than r? [#permalink]

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19 May 2011, 03:03
a+b

x intercept in the 3rd quadrant has the least value.
any value of r in the 3rd quadrant will be > than the intercept value of x.

C
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Re: Is the line’s intercept with axis-x greater than r? [#permalink]

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19 May 2011, 12:59
Very good explanation Bunuel!
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Re: Point (r,s) lies on the line L. Is the line s intercept with [#permalink]

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31 Aug 2013, 06:23
Bumping for review and further discussion.
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Re: Point (r,s) lies on the line L. Is the line s intercept with [#permalink]

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23 Dec 2014, 21:05
Hello from the GMAT Club BumpBot!

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Re: Point (r,s) lies on the line L. Is the line s intercept with [#permalink]

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31 Dec 2015, 19:09
oh damn..did the classic DS mistake..took the info from A, and answered that B is sufficient...
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Re: Point (r,s) lies on the line L. Is the line s intercept with [#permalink]

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11 Jan 2017, 01:13
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).

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Re: Point (r,s) lies on the line L. Is the line s intercept with   [#permalink] 11 Jan 2017, 01:13
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