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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] New post 19 May 2010, 23:54
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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, 02:31, 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] New post 20 May 2010, 00:27
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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.

Answer: C.
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Re: Is the line’s intercept with axis-x greater than r? [#permalink] New post 01 Nov 2010, 04:16
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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
Ques.jpg [ 17.47 KiB | Viewed 2054 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
Ques1.jpg [ 9.6 KiB | Viewed 2050 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] New post 19 May 2011, 02:03
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.

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Re: Is the line’s intercept with axis-x greater than r? [#permalink] New post 19 May 2011, 11:59
Very good explanation Bunuel!
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Re: Point (r,s) lies on the line L. Is the line s intercept with [#permalink] New post 31 Aug 2013, 05:23
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Re: Point (r,s) lies on the line L. Is the line s intercept with   [#permalink] 31 Aug 2013, 05:23
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