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 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.
It appears that you are browsing the GMAT Club forum unregistered!
Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club
Registration gives you:
Tests
Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.
Applicant Stats
View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more
Books/Downloads
Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!
Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:
Re: 179. If line l passes through point (m,– n), is the slope of [#permalink]
15 Feb 2011, 20:57
E. There are an infinite number of lines of every possible slope that can pass through a point. You need a second point to determine the slope of a line and neither question helps.
Re: 179. If line l passes through point (m,– n), is the slope of [#permalink]
16 Feb 2011, 07:01
subhashghosh wrote:
Hi
For Case I
statement tells us: line also passes through; {-m,n} = {-1,1}
Slope of a line passing through {1,1} and {1,-1} would be undefined. (y2-y1)/(x2-x1) = -1-1/1-1 = -2/0 = undefined
n = -1, right ?
And the denominator is not equal to 0, not sure if I'm making a mistake in reading this ?
I am not sure what are you trying to ask!!!
Let me rephrase few things in caseI:
1: Case: I
m and n can literally have any value; Let's use the following values for m and n
m=1 n=-1
so what is {m,-n}
m=1 -n = -(-1) = +1
So; the line passes through (1,1), say point P
statement tells us: line also passes through; {-m,n} m=1; -m = -1 n=-1
Line also passes through (1,-1), say point Q
Slope of a line passing through two points P(1,1)=(x1,y1) and Q(1,-1)=(x2,y2) can be defined as;
m = (y2-y1)/(x2-x1)
For the above two points P and Q; what are our x1,y1,x2,y2
x1=1 y1=1 x2=1 y2=-1
(y2-y1)/(x2-x1) = -1-1/1-1 = -2/0 = if 0 is in denominator; the slope becomes undefined. Means; no slope.
You can see that this line that we are talking about passes through (1,1) and (1,-1). It is a line parallel to y axis. There is no slanting in the line and thus has no slope. _________________
Re: 179. If line l passes through point (m,– n), is the slope of [#permalink]
16 Feb 2011, 07:42
2
This post received KUDOS
Expert's post
banksy wrote:
179. If line l passes through point (m,– n), is the slope of the line negative? (1) The line passes through point (–m, n). (2) mn is negative.
The slope is defined as the ratio of the "rise" divided by the "run" between two points on a line, or in other words, the ratio of the altitude change to the horizontal distance between any two points on the line. Given two points \((x_1,y_1)\) and \((x_2,y_2)\) on a line, the slope \(m\) of the line is: \(m=\frac{y_2-y_1}{x_2-x_1}\)
If line l passes through point (m,– n), is the slope of the line negative?
(1) The line passes through point (–m, n) --> \(slope=\frac{n-(-n)}{-m-m}=-\frac{n}{m}\), so the question becomes: is \(-\frac{n}{m}<0\)? or do \(m\) and \(n\) have the same sign, but we don't know that. Not sufficient.
(2) mn is negative --> \(m\) and \(n\) have the opposite signs --> point (m, -n) is either in I or in III quadrant, though as we have only one point lines passing through it can have negative as well as positive slope. Not sufficient.
(1)+(2) As from (2) \(m\) and \(n\) have the opposite signs the from (1) \(slope=-\frac{n}{m}>0\) and the answer to the question is NO. Sufficient.
Answer: C.
Without any algebra:
If line l passes through point (m,– n), is the slope of the line negative?
(1) The line passes through point (–m, n). Two cases:
A. If m and n are both positive then point (m, -n)=(positive, negative) is in IV quadrant and the second point (-m, n)=(negative, positive) is in II quadrant line passing these two points will have negative slope;
B. If m and n have the opposite signs, for example m positive and n negative, (m, -n)=(positive, positive) is in I quadrant and the second point (-m, n)=(negative, negative) is in III quadrant, line passing these two points will have positive slope (if it's vise-versa, meaning if m is negative and n positive, then we'll still have the same quadrants: (m, -n)=(negative, negative) is in III quadrant and the second point (-m, n)=(positive, positive) is in I quadrant, line passing these two points will have positive slope). Not sufficient.
(2) mn is negative --> m and n have the opposite signs --> point (m, -n) is either in I quadrant in case (m, -n)=(positive, positive) or in III quadrant in case (m, -n)=(negative, negative), though as we have only one point lines passing through it can have negative as well as positive slope. Not sufficient.
(1)+(2) As from (2) m and n have the opposite signs then we have the case B from (1), whihc means that the slope is positive. Sufficient.
Re: 179. If line l passes through point (m,– n), is the slope of [#permalink]
16 Feb 2011, 08:30
fluke wrote:
subhashghosh wrote:
Hi
For Case I
statement tells us: line also passes through; {-m,n} = {-1,1}
Slope of a line passing through {1,1} and {1,-1} would be undefined. (y2-y1)/(x2-x1) = -1-1/1-1 = -2/0 = undefined
n = -1, right ?
And the denominator is not equal to 0, not sure if I'm making a mistake in reading this ?
I am not sure what are you trying to ask!!!
Let me rephrase few things in caseI:
1: Case: I
m and n can literally have any value; Let's use the following values for m and n
m=1 n=-1
so what is {m,-n}
m=1 -n = -(-1) = +1
So; the line passes through (1,1), say point P
statement tells us: line also passes through; {-m,n} m=1; -m = -1 n=-1
Line also passes through (1,-1), say point Q
Slope of a line passing through two points P(1,1)=(x1,y1) and Q(1,-1)=(x2,y2) can be defined as;
m = (y2-y1)/(x2-x1)
For the above two points P and Q; what are our x1,y1,x2,y2
x1=1 y1=1 x2=1 y2=-1
(y2-y1)/(x2-x1) = -1-1/1-1 = -2/0 = if 0 is in denominator; the slope becomes undefined. Means; no slope.
You can see that this line that we are talking about passes through (1,1) and (1,-1). It is a line parallel to y axis. There is no slanting in the line and thus has no slope.
Please ignore both my comments above; they contain calculation errors. case I: P should be (1,1) and Q (-1,-1)
I realized my mistake after Bunuel's explanation. _________________
Re: If line l passes through point (m, n), is the slope of the [#permalink]
28 Dec 2013, 06:21
banksy wrote:
If line l passes through point (m,– n), is the slope of the line negative?
(1) The line passes through point (–m, n). (2) mn is negative.
Let's see
Is slope negative?
Passes through (m,-n) so actually we don't know much. Note that since 'n' is a variable it could be <0 and (m,-(-n) could as well be in the I st quadrant. So don't fall for (m,-n) being in the IV quadrant necessarily
Back to the question
Statement 1
Now if it passes through both (m,-n) and (-m,n) then the line can be either a positive line that is going from quadrant I to III or a negative line going from quadrant II to IV
Insuff
Statement 2
mn<0, this tells us that (m,n) have opposite signs. Therefore, point (m,-n) is either on the II or IV quadrant. But we know nothing about the slope of the line
Together
Since (m,-n) is on the II or IV quadrant then we have the second case in which the line has a negative slope passing through both II and IV quadrant
Hence answer is C
Hope it helps Cheers! J
gmatclubot
Re: If line l passes through point (m, n), is the slope of the
[#permalink]
28 Dec 2013, 06:21
As I’m halfway through my second year now, graduation is now rapidly approaching. I’ve neglected this blog in the last year, mainly because I felt I didn’...
Perhaps known best for its men’s basketball team – winners of five national championships, including last year’s – Duke University is also home to an elite full-time MBA...
Hilary Term has only started and we can feel the heat already. The two weeks have been packed with activities and submissions, giving a peek into what will follow...