Author 
Message 
TAGS:

Hide Tags

Math Expert
Joined: 02 Aug 2009
Posts: 6799

Re: In the xyplane, lines k and l intersect at the point (1,1). Is the y
[#permalink]
Show Tags
07 Aug 2017, 19:37
gary391 wrote: chetan2u wrote: nalinnair wrote: In the \(xy\)plane, lines \(k\) and \(l\) intersect at the point \((1,1)\). Is the \(y\)intercept of \(k\) greater than the \(y\)intercept of \(l\)?
(1) The slope of \(k\) is less than the slope of \(l\). (2) The slope of \(l\) is positive. Hi, An easy question if you are aware of the slopes.... slope is the Increase in Y/ Increase in X.......... OR Vertical increase / Horizontal increase.. If BOTH increase with increase in each other, the SLOPE is Positive... But if Y decreases with increase in X, slope is ive.... so for a point (1,1), a line intercepting above Y as 1, it is ive and with increase in Y, the slope will have even lesser value... At y=1, slope is 0 and at y<1, the slopw will keep increasing as the value of Y increases...
So the relation of yintercept is dependent on slope.. lesser the slope higher is the intercept..(1) The slope of \(k\) is less than the slope of \(l\). As seen above y intercept of line l will be more than line k... Suff (2) The slope of \(l\) is positive. we require to know slope of line k also Insuff A Thanks, chetan2u great response. I am trying to understand the relationship of the slope and y intercept. I think irrespective of the line is increasing or decreasing the slope defines lines steepness w.r.t the y axis. Thus, as we increase the slope our y intercept should increase. [considering both the line don't have a common intersecting point on the yaxis]. Please let me know if my understanding is correct? Hi... If you just take the absolute value, yes with change in x as constant, change in y will be as per your understanding.. The slope depends on change in value of both x and y. Numerator has change in y, so more the change more the slope Denominator has change in x, so less the change more the slope But the slope can be of two types.. From left bottom to right top...... Both change in x and y will be POSITIVE, so slope is POSITIVE From left top to bottom right......Change in y is NEGATIVE and change in x will be POSITIVE, so slope is /+= NEGATIVE even if the absolute value or steepness is MORE
_________________
1) Absolute modulus : http://gmatclub.com/forum/absolutemodulusabetterunderstanding210849.html#p1622372 2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html 3) effects of arithmetic operations : https://gmatclub.com/forum/effectsofarithmeticoperationsonfractions269413.html
GMAT online Tutor



Manager
Joined: 07 Jun 2017
Posts: 103

Re: In the xyplane, lines k and l intersect at the point (1,1). Is the y
[#permalink]
Show Tags
31 Aug 2017, 23:22
please see the attachment, let say Ml= 4 Mk= 6 then the slope of k is less than slope of L y intercept K is greater than L so I think we need both statement to confirm. isn't it? Bunuel or anyone, please correct me
Attachments
line.PNG [ 5.52 KiB  Viewed 849 times ]



Math Expert
Joined: 02 Sep 2009
Posts: 49320

Re: In the xyplane, lines k and l intersect at the point (1,1). Is the y
[#permalink]
Show Tags
31 Aug 2017, 23:40



Manager
Joined: 07 Jun 2017
Posts: 103

Re: In the xyplane, lines k and l intersect at the point (1,1). Is the y
[#permalink]
Show Tags
01 Sep 2017, 00:05
Bunuel wrote: pclawong wrote: please see the attachment, let say Ml= 4 Mk= 6 then the slope of k is less than slope of L y intercept K is greater than L
so I think we need both statement to confirm. isn't it?
Bunuel or anyone, please correct me
If the slope of line L is 4 and the slope of line K is 6, the lines won't look like the way you've drawn. The will look like as below: Oh yea, I mean the red line is K and the blue line is L so then, even the slope L is larger than slope K, y intercept of K is still larger than L am I correct? that means, statement 1 is not suff. we also need to know if it is positive slope or negative



Math Expert
Joined: 02 Sep 2009
Posts: 49320

Re: In the xyplane, lines k and l intersect at the point (1,1)
[#permalink]
Show Tags
01 Sep 2017, 00:24
pclawong wrote: Bunuel wrote: pclawong wrote: please see the attachment, let say Ml= 4 Mk= 6 then the slope of k is less than slope of L y intercept K is greater than L
so I think we need both statement to confirm. isn't it?
Bunuel or anyone, please correct me
If the slope of line L is 4 and the slope of line K is 6, the lines won't look like the way you've drawn. The will look like as below: Oh yea, I mean the red line is K and the blue line is L so then, even the slope L is larger than slope K, y intercept of K is still larger than L am I correct? that means, statement 1 is not suff. we also need to know if it is positive slope or negative (1) says that the slope of \(k\) is less than the slope of \(l\). So, in my image BLUE line is K (slope 6) and the RED line is L (slope 4). As you can see the yintercept of K is greater than the yintercept of L. For (1) the yintercept of K will always be greater than the yintercept of L.
_________________
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



Intern
Joined: 07 Jun 2017
Posts: 16

Re: In the xyplane, lines k and l intersect at the point (1,1). Is the y
[#permalink]
Show Tags
12 Sep 2017, 07:05
(k): y=a1*x+b1 (l): y=a2*x+b2 Line k and l intersect at(1,1): a1+b1=a2+b2 (1): a1<a2 => b1> b2 sufficient (2) a2>0 not sufficient
A
Posted from my mobile device



Intern
Joined: 20 Sep 2015
Posts: 21

Re: In the xyplane, lines k and l intersect at the point (1,1). Is the y
[#permalink]
Show Tags
19 Sep 2017, 09:00
chetan2u wrote: nalinnair wrote: In the \(xy\)plane, lines \(k\) and \(l\) intersect at the point \((1,1)\). Is the \(y\)intercept of \(k\) greater than the \(y\)intercept of \(l\)?
(1) The slope of \(k\) is less than the slope of \(l\). (2) The slope of \(l\) is positive. Hi, An easy question if you are aware of the slopes.... slope is the Increase in Y/ Increase in X.......... OR Vertical increase / Horizontal increase.. If BOTH increase with increase in each other, the SLOPE is Positive... But if Y decreases with increase in X, slope is ive.... so for a point (1,1), a line intercepting above Y as 1, it is ive and with increase in Y, the slope will have even lesser value... At y=1, slope is 0 and at y<1, the slopw will keep increasing as the value of Y increases...
So the relation of yintercept is dependent on slope.. lesser the slope higher is the intercept..(1) The slope of \(k\) is less than the slope of \(l\). As seen above y intercept of line l will be more than line k... Suff (2) The slope of \(l\) is positive. we require to know slope of line k also Insuff A Hi, from (1) Shouldn't the value of yintercept of K always be greater than the yintercept of L?



Intern
Joined: 06 Jul 2017
Posts: 1
Location: India
GPA: 3.5

Re: In the xyplane, lines k and l intersect at the point (1,1). Is the y
[#permalink]
Show Tags
15 Oct 2017, 10:03
gary391 wrote: We can write the equation of the line in slopeintercept form as follow: [Where M is the slope and C is the yintercept]
For Line K : Yk = Mk.Xk +Ck For Line L : Yl = Ml.Xl + Cl
Now, since these lines intercept at (1,1), it must satisfy the equation
For Line K : 1 = Mk.1 +Ck For Line L : 1 = Ml.1 + Cl
=> Mk + Ck = Ml + Cl  (equation I)
Now, From Statement 1  Mk > Ml. Thus, for equation I to hold true. Y intercept of line k must be less than Y intercept of line l (Ck < Cl). Therefore Statement 1 is Sufficient.
Statement 2: Is not sufficient as it doesn't provide information regarding the slope of line L. You can further refine equation: 1 = Mk + ck => Mk = 1Ck. Similarly, Ml = 1Cl. Therefore, from statement 1, Mk < Ml => 1Ck < 1  Cl => Ck > Cl



Manager
Status: Studying Quant
Joined: 04 Sep 2017
Posts: 90
GPA: 3.6
WE: Sales (Computer Software)

Re: In the xyplane, lines k and l intersect at the point (1,1). Is the y
[#permalink]
Show Tags
20 Feb 2018, 04:59
MarkusKarl Asked this on the first page and I have the same question. I played devils advocate and got E. What if the slope of L is 1 and the slope of K is zero or undefined? Then K would never intercept the axis, correct? Thanks in advance for the explanation.
_________________
Would I rather be feared or loved? Easy. Both. I want people to be afraid of how much they love me.
How to sort questions by Topic, Difficulty, and Source: https://gmatclub.com/forum/search.php?view=search_tags



Intern
Joined: 01 Dec 2017
Posts: 14
Location: Italy
GPA: 4

Re: In the xyplane, lines k and l intersect at the point (1,1). Is the y
[#permalink]
Show Tags
03 Mar 2018, 08:31
I agree with msurls, if for line K we have equation X= costant, how do you define the slope and therefore the intercept with Y (which doesn't exist) ? Do you consider the slope of a line parallel to Y axis as +infinite or () infinite...? In this case how can you say that 1) is suff, since you don't have any value of yintercept for line k ?



Math Expert
Joined: 02 Sep 2009
Posts: 49320

Re: In the xyplane, lines k and l intersect at the point (1,1). Is the y
[#permalink]
Show Tags
05 Mar 2018, 01:13
teone83 wrote: I agree with msurls, if for line K we have equation X= costant, how do you define the slope and therefore the intercept with Y (which doesn't exist) ? Do you consider the slope of a line parallel to Y axis as +infinite or () infinite...? In this case how can you say that 1) is suff, since you don't have any value of yintercept for line k ? A vertical line has no slope. Or put another way, for a vertical line the slope is undefined. This, by the way, does NOT mean that its slope is 0, horizontal lines has slope equal to 0. Statement (1) says that " The slope of k is less than the slope of l". If any of the lines were vertical, their slopes would be undefined and it would not make sense to compare an undefined slope to anything. Thus, (1) implies that neither of the lines is vertical.
_________________
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



Math Expert
Joined: 02 Sep 2009
Posts: 49320

Re: In the xyplane, lines k and l intersect at the point (1,1). Is the y
[#permalink]
Show Tags
05 Mar 2018, 01:17
Bunuel wrote: teone83 wrote: I agree with msurls, if for line K we have equation X= costant, how do you define the slope and therefore the intercept with Y (which doesn't exist) ? Do you consider the slope of a line parallel to Y axis as +infinite or () infinite...? In this case how can you say that 1) is suff, since you don't have any value of yintercept for line k ? A vertical line has no slope. Or put another way, for a vertical line the slope is undefined. This, by the way, does NOT mean that its slope is 0, horizontal lines has slope equal to 0. Statement (1) says that " The slope of k is less than the slope of l". If any of the lines were vertical, their slopes would be undefined and it would not make sense to compare an undefined slope to anything. Thus, (1) implies that neither of the lines is vertical. 24. Coordinate Geometry For other subjects: ALL YOU NEED FOR QUANT ! ! !Ultimate GMAT Quantitative MegathreadHope it helps.
_________________
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



Intern
Joined: 13 Nov 2011
Posts: 45
Location: United States
GMAT 1: 620 Q41 V35 GMAT 2: 640 Q40 V38 GMAT 3: 630 Q40 V36 GMAT 4: 700 Q47 V39
GPA: 3.81

Re: In the xyplane, lines k and l intersect at the point (1,1). Is the y
[#permalink]
Show Tags
11 May 2018, 14:31
gary391 wrote: We can write the equation of the line in slopeintercept form as follow: [Where M is the slope and C is the yintercept]
For Line K : Yk = Mk.Xk +Ck For Line L : Yl = Ml.Xl + Cl
Now, since these lines intercept at (1,1), it must satisfy the equation
For Line K : 1 = Mk.1 +Ck For Line L : 1 = Ml.1 + Cl
=> Mk + Ck = Ml + Cl  (equation I)
Now, From Statement 1  Mk > Ml. Thus, for equation I to hold true. Y intercept of line k must be less than Y intercept of line l (Ck < Cl). Therefore Statement 1 is Sufficient.
Statement 2: Is not sufficient as it doesn't provide information regarding the slope of line L. No offense, but I think that more than 1 person here slightly misread statement 1. In other words, Mk < Ml according to the statement. So, the following is what I think: From statement 1 > Mk < Ml. Thus for equation I to hold true the Y intercept of line k must be > the Y intercept of line l. (Ck > Cl). Therefore, statement 1 is sufficient.




Re: In the xyplane, lines k and l intersect at the point (1,1). Is the y &nbs
[#permalink]
11 May 2018, 14:31



Go to page
Previous
1 2
[ 33 posts ]



