Author 
Message 
TAGS:

Hide Tags

Director
Status: Up again.
Joined: 31 Oct 2010
Posts: 519
Concentration: Strategy, Operations
GMAT 1: 710 Q48 V40 GMAT 2: 740 Q49 V42

If m represents the slope of a line in the coordinate geom [#permalink]
Show Tags
01 Jul 2013, 07:06
1
This post received KUDOS
9
This post was BOOKMARKED
Question Stats:
48% (00:40) correct 52% (00:31) wrong based on 495 sessions
HideShow timer Statistics
If m represents the slope of a line in the coordinate geometry plane, does the line intersect quadrant III? 1. \(m= m\) 2. \(m^2=3m\)
Official Answer and Stats are available only to registered users. Register/ Login.
_________________
My GMAT debrief: http://gmatclub.com/forum/from620to710mygmatjourney114437.html



VP
Status: Far, far away!
Joined: 02 Sep 2012
Posts: 1115
Location: Italy
Concentration: Finance, Entrepreneurship
GPA: 3.8

Re: If m represents the slope of a line in the coordinate geom [#permalink]
Show Tags
01 Jul 2013, 07:22
1
This post received KUDOS
2
This post was BOOKMARKED
If m represents the slope of a line in the coordinate geometry plane, does the line intersect quadrant III?1. \(m= m\)So m is \(\geq{ 0}\). If m is 0, the line is straight, hence it can or cannot intersect the III quadrant. Consider \(y=100\) (yes) and \(y=100\) (no) 2. \(m^2=3m\)\(m^23m=0\) so \(m=3\) or \(m=0\). If m=3, it will intersect the III quadrant, but if m=0 it can or cannot. 1+2) Since m=0 is common, both statements are still not sufficient
_________________
It is beyond a doubt that all our knowledge that begins with experience.
Kant , Critique of Pure Reason Tips and tricks: Inequalities , Mixture  Review: MGMAT workshop Strategy: SmartGMAT v1.0  Questions: Verbal challenge SC III CR New SC set out !! , My QuantRules for Posting in the Verbal Forum  Rules for Posting in the Quant Forum[/size][/color][/b]



Math Expert
Joined: 02 Sep 2009
Posts: 44421

Re: If m represents the slope of a line in the coordinate geom [#permalink]
Show Tags
01 Jul 2013, 08:05
2
This post received KUDOS
Expert's post
10
This post was BOOKMARKED
gmatpapa wrote: If m represents the slope of a line in the coordinate geometry plane, does the line intersect quadrant III?
1. \(m= m\) 2. \(m^2=3m\) Theory:1. If the slope of line is negative, line WILL intersect quadrants II and IV. X and Y intersects of the line with negative slope have the same sign. Therefore if X and Y intersects are positive, line intersects the quadrant I too, if negative quadrant III. 2. If the slope of line is positive, line WILL intersect quadrants I and III. Y and X intersects of the line with positive slope have opposite signs. Therefore if X intersect is negative, line intersects the quadrant II too, if positive quadrant IV. 3. Every line (but the one crosses origin OR parallel to X or Y axis OR X and Y axis themselves) crosses three quadrants. Only the line which crosses origin (0,0) OR is parallel of either of axis crosses two quadrants. 4. If a line is horizontal the line has slope 0, is parallel to Xaxis and crosses quadrant I and II, if the Y intersect is positive OR quadrants III and IV, if the Y intersect is negative. Equation of such line is y=b, where b is y intersect. 5. If a line is vertical, the slope is not defined, line is parallel to Yaxis and crosses quadrant I and IV, if the X intersect is positive and quadrant II and III, if the X intersect is negative. Equation of such line is x=a, where a is xintercept. Similar questions to practice:inthexycoordinatesystemdoanypointsonlinekliein127635.htmlintherectangularcoordinatesystemshowndoesthelinek67693.htmlinthexyplaneistheslopeoflinelgreaterthanthe126941.htmlinthexyplaneiflinekhasnegativeslopeandpasses135197.htmliftheslopesofthelinel1andl2areofthesamesignis126759.htmllinesintersectinganglesm08q1566826.html#p1235093linesrandslieinthexyplaneistheyinterceptoflin153952.htmlTheory on Coordinate Geometry: mathcoordinategeometry87652.htmlDS Coordinate Geometry Problems to practice: search.php?search_id=tag&tag_id=41PS Coordinate Geometry Problems to practice: search.php?search_id=tag&tag_id=62[/textarea]
_________________
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



Senior Manager
Joined: 13 May 2013
Posts: 453

Re: If m represents the slope of a line in the coordinate geom [#permalink]
Show Tags
20 Jul 2013, 11:54
Zarrolou wrote: If m represents the slope of a line in the coordinate geometry plane, does the line intersect quadrant III?
1. \(m= m\) So m is \(\geq{ 0}\). If m is 0, the line is straight, hence it can or cannot intersect the III quadrant. Consider \(y=100\) (yes) and \(y=100\) (no)
2. \(m^2=3m\) \(m^23m=0\) so \(m=3\) or \(m=0\). If m=3, it will intersect the III quadrant, but if m=0 it can or cannot.
1+2) Since m=0 is common, both statements are still not sufficient Two questions: First, in #1 you said that if the slope is negative 100 it intersects III but in #2 you said if it is positive 3 it intersects III. Doesn't the sign change mean it intersect different quadrants? Second, if both 1 and 2 share a single common value (in this case, 0) doesn't that mean we have a single, definitive answer? Thanks!



Senior Manager
Joined: 13 May 2013
Posts: 453

Re: If m represents the slope of a line in the coordinate geom [#permalink]
Show Tags
20 Jul 2013, 12:02
1
This post was BOOKMARKED
If m represents the slope of a line in the coordinate geometry plane, does the line intersect quadrant III?
1. m= m M>=0
The slope could be equal to zero in which case the line runs flat along the x axis and does not pass through QIII.
The slope could be equal to 5 in which case the line would pass through QIII at some point. INSUFFICIENT
2. m^2=3m
M^2  3m = 0
m=0, m=3. As with above, if m=0 it will not pass through QIII but if m=3 then it will. INSUFFICIENT
1+2 #1 tells us m>=0 and #2 tells us m=0 OR m=3 which is redundant when considering #1. Therefore, m may or may not pass through QIII. INSUFFICIENT
(E)



Math Expert
Joined: 02 Sep 2009
Posts: 44421

Re: If m represents the slope of a line in the coordinate geom [#permalink]
Show Tags
20 Jul 2013, 12:03
WholeLottaLove wrote: Zarrolou wrote: If m represents the slope of a line in the coordinate geometry plane, does the line intersect quadrant III?
1. \(m= m\) So m is \(\geq{ 0}\). If m is 0, the line is straight, hence it can or cannot intersect the III quadrant. Consider \(y=100\) (yes) and \(y=100\) (no)
2. \(m^2=3m\) \(m^23m=0\) so \(m=3\) or \(m=0\). If m=3, it will intersect the III quadrant, but if m=0 it can or cannot.
1+2) Since m=0 is common, both statements are still not sufficient Two questions: First, in #1 you said that if the slope is negative 100 it intersects III but in #2 you said if it is positive 3 it intersects III. Doesn't the sign change mean it intersect different quadrants? Second, if both 1 and 2 share a single common value (in this case, 0) doesn't that mean we have a single, definitive answer? Thanks! Please read this post: ifmrepresentstheslopeofalineinthecoordinategeom155176.html#p1241612Next, when considering the statements we have that m=0, which means that the line is horizontal. The question is "does the line intersect quadrant III?" not what is the value of m. Horizontal line may or may not intersect quadrant III. Hope it's clear.
_________________
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



VP
Status: Far, far away!
Joined: 02 Sep 2012
Posts: 1115
Location: Italy
Concentration: Finance, Entrepreneurship
GPA: 3.8

Re: If m represents the slope of a line in the coordinate geom [#permalink]
Show Tags
20 Jul 2013, 12:04
1
This post received KUDOS
WholeLottaLove wrote: Zarrolou wrote: If m represents the slope of a line in the coordinate geometry plane, does the line intersect quadrant III?
1. \(m= m\) So m is \(\geq{ 0}\). If m is 0, the line is straight, hence it can or cannot intersect the III quadrant. Consider \(y=100\) (yes) and \(y=100\) (no)
2. \(m^2=3m\) \(m^23m=0\) so \(m=3\) or \(m=0\). If m=3, it will intersect the III quadrant, but if m=0 it can or cannot.
1+2) Since m=0 is common, both statements are still not sufficient Two questions: First, in #1 you said that if the slope is negative 100 it intersects III but in #2 you said if it is positive 3 it intersects III. Doesn't the sign change mean it intersect different quadrants? Second, if both 1 and 2 share a single common value (in this case, 0) doesn't that mean we have a single, definitive answer? Thanks! I think you are confusing the parts of the equation of the line. \(y=Slope(=m)*X+k\)<== this is the standard for of a line. These two lines have NO SLOPE (they are straight, horizontal, parallel to the xaxis) => m=0. \(y=100\) \(y=100\). y=100 is a straight line that passes through the III and IV quadrant; y=100 passes through the I and II quadrant. (refer to the image) If we know that m=0 both y=100 and y=100 are still valid.
Attachments
Im.JPG [ 12.14 KiB  Viewed 7073 times ]
_________________
It is beyond a doubt that all our knowledge that begins with experience.
Kant , Critique of Pure Reason Tips and tricks: Inequalities , Mixture  Review: MGMAT workshop Strategy: SmartGMAT v1.0  Questions: Verbal challenge SC III CR New SC set out !! , My QuantRules for Posting in the Verbal Forum  Rules for Posting in the Quant Forum[/size][/color][/b]



Senior Manager
Joined: 13 May 2013
Posts: 453

Re: If m represents the slope of a line in the coordinate geom [#permalink]
Show Tags
20 Jul 2013, 12:13
Bunuel wrote: WholeLottaLove wrote: Zarrolou wrote: If m represents the slope of a line in the coordinate geometry plane, does the line intersect quadrant III?
1. \(m= m\) So m is \(\geq{ 0}\). If m is 0, the line is straight, hence it can or cannot intersect the III quadrant. Consider \(y=100\) (yes) and \(y=100\) (no)
2. \(m^2=3m\) \(m^23m=0\) so \(m=3\) or \(m=0\). If m=3, it will intersect the III quadrant, but if m=0 it can or cannot.
1+2) Since m=0 is common, both statements are still not sufficient Two questions: First, in #1 you said that if the slope is negative 100 it intersects III but in #2 you said if it is positive 3 it intersects III. Doesn't the sign change mean it intersect different quadrants? Second, if both 1 and 2 share a single common value (in this case, 0) doesn't that mean we have a single, definitive answer? Thanks! Please read this post: ifmrepresentstheslopeofalineinthecoordinategeom155176.html#p1241612Next, when considering the statements we have that m=0, which means that the line is horizontal. The question is "does the line intersect quadrant III?" not what is the value of m. Horizontal line may or may not intersect quadrant III.Hope it's clear. Ahhh. It's been a while since I've done anything related to coordinate geometry (trying to nail modules down cold haha!) Now I remember. Thanks.



Senior Manager
Joined: 13 May 2013
Posts: 453

Re: If m represents the slope of a line in the coordinate geom [#permalink]
Show Tags
20 Jul 2013, 12:58
This is an updated version of my original solution found above.
If m represents the slope of a line in the coordinate geometry plane, does the line intersect quadrant III?
1. m= m M>=0
If m = 0 then it has no slope. However, it still may or may not pass through QIII. If y = 2 then it would be a flat line passing through QI and QII. If y = 2 then it would be a flat line passing through QIII and QIV. Furthermore, if the line did have a slope, it may or may not pass through QIII. For example, if it had a slope of 2 it would pass through QIII (assuming it has infinite length) but if the slope was negative it may not ever pass through QIII) INSUFFICIENT
2. m^2=3m
M^2  3m = 0
m=0, m=3. If the slope is zero then it may or may not pass through QIII. We would need to know it's y coordinate to determine that. If the slope is positive 3, then it would pass through QIII INSUFFICIENT
1+2 Both 1 and 2 tell us that the slope could be zero or greater than zero. If the slope is zero then it may or may not pass through QIII. If it is greater than zero it will. We cannot determine if it passes through QIII or not. INSUFFICIENT
(E)



Director
Joined: 25 Apr 2012
Posts: 720
Location: India
GPA: 3.21
WE: Business Development (Other)

Re: If m represents the slope of a line in the coordinate geom [#permalink]
Show Tags
21 Jul 2013, 03:38
Zarrolou wrote: If m represents the slope of a line in the coordinate geometry plane, does the line intersect quadrant III?
1. \(m= m\) So m is \(\geq{ 0}\). If m is 0, the line is straight, hence it can or cannot intersect the III quadrant. Consider \(y=100\) (yes) and \(y=100\) (no)
2. \(m^2=3m\) \(m^23m=0\) so \(m=3\) or \(m=0\). If m=3, it will intersect the III quadrant, but if m=0 it can or cannot.
1+2) Since m=0 is common, both statements are still not sufficient Hi Zarrolou, St1 m= m can also be inferred as m=m= m since m=m this implies m>/ 0 or m <0 Combining with statement 2 we get m=0 as common and again answer can be yes or no depending upon value of y. Will the above interpretation of st1 will be correct. thanks Mridul
_________________
“If you can't fly then run, if you can't run then walk, if you can't walk then crawl, but whatever you do you have to keep moving forward.”



Math Expert
Joined: 02 Sep 2009
Posts: 44421

Re: If m represents the slope of a line in the coordinate geom [#permalink]
Show Tags
21 Jul 2013, 03:50
mridulparashar1 wrote: Zarrolou wrote: If m represents the slope of a line in the coordinate geometry plane, does the line intersect quadrant III?
1. \(m= m\) So m is \(\geq{ 0}\). If m is 0, the line is straight, hence it can or cannot intersect the III quadrant. Consider \(y=100\) (yes) and \(y=100\) (no)
2. \(m^2=3m\) \(m^23m=0\) so \(m=3\) or \(m=0\). If m=3, it will intersect the III quadrant, but if m=0 it can or cannot.
1+2) Since m=0 is common, both statements are still not sufficient Hi Zarrolou, St1 m= m can also be inferred as m=m= m since m=m this implies m>/ 0 or m <0 Combining with statement 2 we get m=0 as common and again answer can be yes or no depending upon value of y. Will the above interpretation of st1 will be correct. thanks Mridul No, that's not correct. \(m=m\) implies that \(m\geq{0}\) ONLY. What does m>/ 0 or m <0 even mean? It gives all values possible, doesn't it? Absolute value properties:When \(x \leq{0}\) then \(x=x\), or more generally when \(some \ expression\leq{0}\) then \(some \ expression={(some \ expression)}\). For example: \(5=5=(5)\); When \(x \geq{0}\) then \(x=x\), or more generally when \(some \ expression\geq{0}\) then \(some \ expression={some \ expression}\). For example: \(5=5\).
_________________
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



Manager
Joined: 22 Feb 2016
Posts: 102
Location: India
Concentration: Economics, Healthcare
GMAT 1: 690 Q42 V47 GMAT 2: 710 Q47 V39
GPA: 3.57

Re: If m represents the slope of a line in the coordinate geom [#permalink]
Show Tags
18 Oct 2016, 19:19
1
This post received KUDOS
My 2 cents for this long discussion. statement 1= M=M in this case m can be 0 or +ve or ve NS
Statement 2= m^2=3m hence m can be 3 or 0 NS
Combining M can be +ve or 0 thus E is the correct answer.



Intern
Joined: 25 Nov 2011
Posts: 15
Location: India
Concentration: General Management, Entrepreneurship
WE: Design (Other)

Re: If m represents the slope of a line in the coordinate geom [#permalink]
Show Tags
18 Oct 2016, 19:57
gmatpapa wrote: If m represents the slope of a line in the coordinate geometry plane, does the line intersect quadrant III?
1. \(m= m\) 2. \(m^2=3m\) Statement 1. \(m= m\) Analyzing the modulus : Any number= either 0 or + That implies the value of m can be either 0 or + Now if the slope of a line is either 0 or +, it can intersect or not intersect Quadrant III. As Slope = Change in y/change in X Scenario A: if ^y =+ and ^X=+, slope =+ ; Slope will intersect Scenario B: if ^y = and ^X=, slope =+ ; Slope will intersect Scenario C: if ^y =0 and ^X=, slope =0 ; Slope will not intersect So, It is not sufficient. Statement 2. \(m^2=3m\)[/quote] This statement also implies m is either + or 0 as product of a positive no. and a variable is equal to a square number. Therefore again it is a restatement of earlier 1. So, It is also not sufficient. Therefore , Answer E.



NonHuman User
Joined: 09 Sep 2013
Posts: 6554

Re: If m represents the slope of a line in the coordinate geom [#permalink]
Show Tags
19 Nov 2017, 12:07
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 m represents the slope of a line in the coordinate geom
[#permalink]
19 Nov 2017, 12:07






