Author 
Message 
TAGS:

Hide Tags

Intern
Joined: 04 Dec 2009
Posts: 19

In the xyplane, line k passes through the point (1, 1) and line m
[#permalink]
Show Tags
11 Jun 2010, 07:24
Question Stats:
64% (01:49) correct 36% (01:33) wrong based on 500 sessions
HideShow timer Statistics
In the xyplane, line k passes through the point (1, 1) and line m passes through the point (1, 1). Are the lines k and m perpendicular to each other ? (1) Lines k and m intersect at the point (1, 1) (2) Line k intersects the xaxis at the point (1, 0)
Official Answer and Stats are available only to registered users. Register/ Login.




Math Expert
Joined: 02 Sep 2009
Posts: 49992

Re: In the xyplane, line k passes through the point (1, 1) and line m
[#permalink]
Show Tags
11 Jun 2010, 08:01
gautamsubrahmanyam wrote: In the xyplane ,line k passes through the point (1,1) and line m passes through the point (1,1).Are the lines k and m perpendicular to each other
(1) Lines k and m intersect at the point (1,1) (2) Line k intersects the x axis at the point (1,0)
Please help on this DS problem For one line to be perpendicular to another, their slopes must be negative reciprocals of each other (if slope of one line is \(m\) than the slope of the line perpendicular to this line is \(\frac{1}{m}\)). In other words, the two lines are perpendicular if and only the product of their slopes is \(1\). So basically the question is can we somehow calculate the slopes of these lines. From stem we have one point for each line. (1) gives us the second point of line \(k\), hence we can get the slope of this line, but we still know only one point of line \(m\). Not sufficient. (2) again gives the second point of line \(k\), hence we can get the slope of this line, but we still know only one point of line \(m\). Not sufficient. (1)+(2) we can derive the slope of line \(k\) but for line \(m\) we still have only one point, hence we can not calculate its slope. Not sufficient. Answer: E. For more on this issue please check Coordinate Geometry chapter of Math Book (link in my signature). ALSO:
_________________
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: 02 Nov 2009
Posts: 112

Re: In the xyplane, line k passes through the point (1, 1) and line m
[#permalink]
Show Tags
16 May 2012, 08:05
I did not understand why you said you can find out only line K slope from statement 1  why not m sorry but not able to follow please help



Math Expert
Joined: 02 Sep 2009
Posts: 49992

Re: In the xyplane, line k passes through the point (1, 1) and line m
[#permalink]
Show Tags
16 May 2012, 09:17



Intern
Joined: 20 May 2012
Posts: 18

Re: In the xyplane, line k passes through the point (1, 1) and line m
[#permalink]
Show Tags
07 Jun 2012, 16:36
Could you tell me how to determine whether the lines are perpendicular just in general??



Math Expert
Joined: 02 Sep 2009
Posts: 49992

In the xyplane, line k passes through the point (1, 1) and line m
[#permalink]
Show Tags
07 Jun 2012, 16:46



SVP
Joined: 06 Sep 2013
Posts: 1764
Concentration: Finance

Re: In the xyplane, line k passes through the point (1, 1) and line m
[#permalink]
Show Tags
20 Dec 2013, 12:32
gautamsubrahmanyam wrote: In the xyplane, line k passes through the point (1,1) and line m passes through the point (1,1). Are the lines k and m perpendicular to each other
(1) Lines k and m intersect at the point (1,1) (2) Line k intersects the x axis at the point (1,0) They don't mention that they have to be different lines do they? Can it be the same vertical line as well? Thanks Cheers! J



Math Expert
Joined: 02 Sep 2009
Posts: 49992

Re: In the xyplane, line k passes through the point (1, 1) and line m
[#permalink]
Show Tags
21 Dec 2013, 05:47



Veritas Prep GMAT Instructor
Joined: 15 Jul 2015
Posts: 110
GPA: 3.62
WE: Corporate Finance (Consulting)

Re: In xy plane, line k passes through (1,1) and m through (1, 1). Are
[#permalink]
Show Tags
27 Oct 2015, 11:54
Timmimmit wrote: First time I am posting in the forum. I could not find the solution to this question from GMATPrep. Please help me.
In xy plane, line k passes through (1,1) and m through (1, 1). Are lines k and m perpendicular?
a. k and m intersect at (1, 1)
b. k intersects x –axis at (1, 0) From the question, all we know are points on each k and m. To determine whether the lines are perpindicular, we need to know the slopes of each line. Stmt 1) tells us that k goes through (1,1) and (1, 1), therefore we can figure out its slope. But we still have no information to determine the slope of line m. NOT SUFFICIENT Stmt 2) gives us no informatin that we cannot glean from Stmt 1. NOT SUFFICIENT Using both Stmts, we still cannot determine the slope of line m. NOT SUFFICIENT Correct answer is E
_________________
Dennis Veritas Prep  GMAT Instructor
Get started with Veritas Prep GMAT On Demand for $199
Veritas Prep Reviews



CEO
Joined: 12 Sep 2015
Posts: 3009
Location: Canada

In xy plane, line k passes through (1,1) and m through (1, 1). Are
[#permalink]
Show Tags
Updated on: 16 Apr 2018, 13:01
Timmimmit wrote: First time I am posting in the forum. I could not find the solution to this question from GMATPrep. Please help me.
In xy plane, line k passes through (1,1) and m through (1, 1). Are lines k and m perpendicular?
a. k and m intersect at (1, 1)
b. k intersects x –axis at (1, 0) Target question: Are lines K and m perpendicular to each other?IMPORTANT: Since line K passes through the point (1, 1), statements 1 and 2 both have the same effect of "locking" line K into exactly one position. In fact, statements 1 and 2 essentially provide the exact same information. As such, it's either the case that each statement is sufficient (D) or each statement is not sufficient (E). Since neither statement locks line M into any certain position, line M is free to be in lots of different positions, as long as it passes through the point (1, 1) Okay, let's jump right to . . . Statements 1 and 2 combined: Here are two possible scenarios that satisfy statements 1 and 2. Scenario a: In this instance, lines M and K are perpendicular. Scenario b: In this instance, lines M and K are not perpendicular. Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT Answer = E Aside: This concept of "locking in" shapes on Geometry DS questions is discussed in much greater detail in our free video: http://www.gmatprepnow.com/module/gmat ... cy?id=1103 Cheers, Brent
_________________
Brent Hanneson – GMATPrepNow.com
Sign up for our free Question of the Day emails
Originally posted by GMATPrepNow on 27 Oct 2015, 12:20.
Last edited by GMATPrepNow on 16 Apr 2018, 13:01, edited 1 time in total.



Manager
Status: One Last Shot !!!
Joined: 04 May 2014
Posts: 239
Location: India
Concentration: Marketing, Social Entrepreneurship
GMAT 1: 630 Q44 V32 GMAT 2: 680 Q47 V35

Re: In xy plane, line k passes through (1,1) and m through (1, 1). Are
[#permalink]
Show Tags
27 Oct 2015, 18:21
Timmimmit wrote: In xy plane, line k passes through (1,1) and m through (1, 1). Are lines k and m perpendicular?
(1) k and m intersect at (1, 1) (2) k intersects x –axis at (1, 0) This question can be efficiently solved by plotting (imagining) the graph of the lines k and m, rather than trying to find out slopes of the lines algebraically. To know the slope of a line, we should be able to 'fix' the line on the XY plane. And to fix a line we need at least two points that the line passes through. With this in mind, lets see what's given to us. Question stem: k passes through \((1,1)\), and m passes through \((1,1)\) At this point none of the lines are fixed. Both of them can rotate \(360^{\circ}\) about the points they are passing through. S1) This gives another point for line K. So now we have two points that line k passes through \((1,1)\) and \((1,1)\). Now we can fix our line k. (at this point we realize that like k is parallel to Yaxis). But with this, we still do not have line m fixed. We cannot comment about their angle. Hence insufficient. S2) This given yet another point that the line k passes through. This is not required as our like k is already fixed. All we needed was another point on line m to fix it. Since we do not have any info on line m and it can still rotate about the point \((1,1)\) and can take any angle w.r.t. line k, this info is insufficient. S1+S2) As we do not have any new info regarding line m and we cant fix it yet, this is again insufficient. Hence, the answer is E. Hope that helps.
_________________
One Kudos for an everlasting piece of knowledge is not a bad deal at all...
 Twenty years from now you will be more disappointed by the things you didn't do than by the ones you did do. So throw off the bowlines. Sail away from the safe harbor. Catch the trade winds in your sails. Explore. Dream. Discover. Mark Twain



Director
Joined: 04 Jun 2016
Posts: 569

In the xyplane, line k passes through the point (1, 1) and line m
[#permalink]
Show Tags
14 Jul 2016, 23:12
gautamsubrahmanyam wrote: In the xyplane, line k passes through the point (1, 1) and line m passes through the point (1, 1). Are the lines k and m perpendicular to each other ? (1) Lines k and m intersect at the point (1, 1) (2) Line k intersects the xaxis at the point (1, 0) Two lines are parallel only if their slopes are inverse reciprocal of each other. (1) Lines k and m intersect at the point (1, 1) Using the (x,y) pair of (1,1) and other (x,y) pair of (1,1) of line k from the question stem we can see that the slope is undefined. Slope of K = \(\frac{1(1)}{11} = \frac{2}{0} ==> undefined\) Meaning Line K is parallel to Y axis and pass through the x axis at x=1, y=0 INSUFFICIENT we have no info about the slope of line K (2) Line k intersects the xaxis at the point (1, 0) We already know from statement 1 that k passes from x=1. INSUFFICIENT Merging both statement WE NEED SLOPE OF LINE M But there are only one (x,y) pair given for line M and thus we cannot calculate the slope. and thus cannot compare it with slope of line k Merging also doesn't gives any new information Hence insufficient ANSWER IS E
_________________
Posting an answer without an explanation is "GOD COMPLEX". The world doesn't need any more gods. Please explain you answers properly. FINAL GOODBYE : 17th SEPTEMBER 2016. .. 16 March 2017  I am back but for all purposes please consider me semiretired.



CEO
Joined: 12 Sep 2015
Posts: 3009
Location: Canada

In the xyplane, line k passes through the point (1, 1) and line m
[#permalink]
Show Tags
Updated on: 16 Apr 2018, 12:18
gautamsubrahmanyam wrote: In the xyplane, line k passes through the point (1, 1) and line m passes through the point (1, 1). Are the lines k and m perpendicular to each other ?
(1) Lines k and m intersect at the point (1, 1) (2) Line k intersects the xaxis at the point (1, 0) Target question: Are lines K and m perpendicular to each other?IMPORTANT: Since line K passes through the point (1, 1), statements 1 and 2 both have the same effect of "locking" line K into exactly one position. In fact, statements 1 and 2 essentially provide the exact same information. As such, it's either the case that each statement is sufficient (D) or each statement is not sufficient (E). Since neither statement locks line M into any certain position, line M is free to be in lots of different positions, as long as it passes through the point (1, 1) Okay, let's jump right to . . . Statements 1 and 2 combined: Here are two possible scenarios that satisfy statements 1 and 2. Scenario a: In this instance, lines M and K are perpendicular. Scenario b: In this instance, lines M and K are not perpendicular. Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT Answer = E Cheers, Brent
_________________
Brent Hanneson – GMATPrepNow.com
Sign up for our free Question of the Day emails
Originally posted by GMATPrepNow on 18 Nov 2017, 11:19.
Last edited by GMATPrepNow on 16 Apr 2018, 12:18, edited 1 time in total.




In the xyplane, line k passes through the point (1, 1) and line m &nbs
[#permalink]
18 Nov 2017, 11:19






