Author 
Message 
TAGS:

Hide Tags

Manager
Joined: 10 Feb 2011
Posts: 109

If line l passes through point (m, n), is the slope of the
[#permalink]
Show Tags
15 Feb 2011, 13:12
Question Stats:
50% (02:12) correct 50% (01:19) wrong based on 116 sessions
HideShow timer Statistics
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.
Official Answer and Stats are available only to registered users. Register/ Login.



Manager
Joined: 07 Jun 2010
Posts: 81

Re: 179. If line l passes through point (m,– n), is the slope of
[#permalink]
Show Tags
15 Feb 2011, 21:57
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.



Manager
Joined: 10 Feb 2011
Posts: 109

Re: 179. If line l passes through point (m,– n), is the slope of
[#permalink]
Show Tags
16 Feb 2011, 02:28
but we got 2 points here: (m,n) and (m, n) throw which passes a line L, no?...



Retired Moderator
Joined: 20 Dec 2010
Posts: 1868

Re: 179. If line l passes through point (m,– n), is the slope of
[#permalink]
Show Tags
16 Feb 2011, 02:46
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. Use sample numbers and test: 1: Case: I Let's put some values for m and n m=1 n=1 so{m,n} = {1,1} 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. (y2y1)/(x2x1) = 11/11 = 2/0 = undefined Case II: m=1 n=1 so{m,n} = {1,1} statement tells us: line also passes through; {m,n} = {1,1} Slope of a line passing through {1,1} and {1,1} would be. (y2y1)/(x2x1) = 1+1/1+1 = 0/2 = 0. Neither +ve nor ve. Case III: m=1 n=1 {m,n} = {1,1} {m,n} = {1,1} Slope = 1+1/11 = 2/2 = 1 Negative. case IV: m=1 n=1 {m,n} = {1,1} {m,n} = {1,1} Slope = 11/1+1 = 2/2=1 Negative Not sufficient. 2. mn is ve. In the above sample set; for caseI and case2, mn is ve and they both are yielding different signs for slopes. Not sufficient. Using both; caseI and caseII from statement1 will result in different types of slopes. Not Sufficient. Ans: "E"
_________________
~fluke
GMAT Club Premium Membership  big benefits and savings



Retired Moderator
Joined: 16 Nov 2010
Posts: 1451
Location: United States (IN)
Concentration: Strategy, Technology

Re: 179. If line l passes through point (m,– n), is the slope of
[#permalink]
Show Tags
16 Feb 2011, 07:41
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. (y2y1)/(x2x1) = 11/11 = 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 ?
_________________
Formula of Life > Achievement/Potential = k * Happiness (where k is a constant)
GMAT Club Premium Membership  big benefits and savings



Retired Moderator
Joined: 20 Dec 2010
Posts: 1868

Re: 179. If line l passes through point (m,– n), is the slope of
[#permalink]
Show Tags
16 Feb 2011, 08:01
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. (y2y1)/(x2x1) = 11/11 = 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 = (y2y1)/(x2x1) For the above two points P and Q; what are our x1,y1,x2,y2 x1=1 y1=1 x2=1 y2=1 (y2y1)/(x2x1) = 11/11 = 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.
_________________
~fluke
GMAT Club Premium Membership  big benefits and savings



Math Expert
Joined: 02 Sep 2009
Posts: 49417

Re: 179. If line l passes through point (m,– n), is the slope of
[#permalink]
Show Tags
16 Feb 2011, 08:42
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: \(m=\frac{y_2y_1}{x_2x_1}\) If line l passes through point (m,– n), is the slope of the line negative?(1) The line passes through point (–m, n) > \(slope=\frac{n(n)}{mm}=\frac{n}{m}\), 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 viseversa, 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. Answer: C. Check Coordinate Geometry chapter of Math Book for more: mathcoordinategeometry87652.html
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



Retired Moderator
Joined: 20 Dec 2010
Posts: 1868

Re: 179. If line l passes through point (m,– n), is the slope of
[#permalink]
Show Tags
16 Feb 2011, 09:30
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. (y2y1)/(x2x1) = 11/11 = 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 = (y2y1)/(x2x1) For the above two points P and Q; what are our x1,y1,x2,y2 x1=1 y1=1 x2=1 y2=1 (y2y1)/(x2x1) = 11/11 = 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.
_________________
~fluke
GMAT Club Premium Membership  big benefits and savings



SVP
Joined: 06 Sep 2013
Posts: 1801
Concentration: Finance

Re: If line l passes through point (m, n), is the slope of the
[#permalink]
Show Tags
28 Dec 2013, 07:21
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



NonHuman User
Joined: 09 Sep 2013
Posts: 8161

Re: If line l passes through point (m, n), is the slope of the
[#permalink]
Show Tags
25 Aug 2018, 09:30
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). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
GMAT Books  GMAT Club Tests  Best Prices on GMAT Courses  GMAT Mobile App  Math Resources  Verbal Resources




Re: If line l passes through point (m, n), is the slope of the &nbs
[#permalink]
25 Aug 2018, 09:30






