GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 20 Oct 2018, 19:02

Close

GMAT Club Daily Prep

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.

Close

Request Expert Reply

Confirm Cancel

If L and K are lines in xy- plane, is the product of the

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Manager
Manager
avatar
Joined: 23 Jan 2008
Posts: 108
If L and K are lines in xy- plane, is the product of the  [#permalink]

Show Tags

New post 31 Jan 2008, 19:24
1
2
00:00
A
B
C
D
E

Difficulty:

  5% (low)

Question Stats:

88% (01:12) correct 12% (01:24) wrong based on 234 sessions

HideShow timer Statistics

If L and K are lines in xy- plane, is the product of the slope of L and K equal to -1?

(1) Line L passes through the origin and the point (1,2).
(2) Line K has x-intercept 4 and y-intercept 2.
Most Helpful Expert Reply
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 50007
Re: If l and K are lines in xy- plane, is the product of the  [#permalink]

Show Tags

New post 16 Jul 2012, 05:42
4
2
We don't need to calculate anything to answer this question.

If L and K are lines in xy- plane, is the product of the slope of l and k equal to -1?

The product of two lines equal to -1 if these lines are perpendicular to each other. So, the question basically asks whether L and K are perpendicular to each other.

Now, if we knew the equations of each line we would be able to answer the question. What do we need to find equation of a line? Since a line is defined by two points, then if we knew any two points of a line then we could get its equatiom

(1) Line L passes through the origin and the point (1,2). We have two points of line L: (0, 0) and (1, 2). So, we can get the equation of line L, though we know nothing about line K. Not sufficient.

(2) Line K has x-intercept 4 and y-intercept 2. We have two points of line K: (4, 0) and (0, 2). So, we can get the equation of line K, though we know nothing about line L. Not sufficient.

(1)+(2) We know both equation, hence we can answer whether the lines are perpendicular to each other. Sufficient.

Answer: C.

venmic wrote:
Can anyone give a better explanation on this one please

Hovv does K have a slope of -1/2 out of novvhere at all

Please any expert


Given two points \((x_1,y_1)\) and \((x_2,y_2)\) on a line, the slope \(m\) of the line is:

\(m=\frac{y_2-y_1}{x_2-x_1}\).

Since x-intercept of line K is 4, then it passes through point (4, 0) and since y-intercept of line K is 2, the it passes through point (0, 2). Hence it's slope is \(m=\frac{2-0}{0-4}=-\frac{1}{2}\).

For more on Coordinate Geometry check: math-coordinate-geometry-87652.html

Hope 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?
Extra-hard Quant Tests with Brilliant Analytics

General Discussion
SVP
SVP
avatar
Joined: 29 Mar 2007
Posts: 2447
Re: DS - if l and k  [#permalink]

Show Tags

New post 31 Jan 2008, 21:15
blog wrote:
If l and K are lines in xy- plane, is the product of the slope of l and k equal to -1?

1. Line l passes through the origin and the point (1,2).
2. Line K has x-intercept 4 and y-intercept 2.



C


1: we dont know anything about the other line but we can find the slope of line l = 2

2: again we dont know the other line's slope but k's is -1/2

Together 2*-1/2= -1

But you could just realize that 1 and 2 are suff together b/c we know the slopes we are going to get a YES OR A NO NOT BOTH. so u could save some time.
SVP
SVP
avatar
Joined: 29 Mar 2007
Posts: 2447
Re: DS - if l and k  [#permalink]

Show Tags

New post 01 Feb 2008, 10:55
blog wrote:
GMATBLACKBELT wrote:
blog wrote:
If l and K are lines in xy- plane, is the product of the slope of l and k equal to -1?

1. Line l passes through the origin and the point (1,2).
2. Line K has x-intercept 4 and y-intercept 2.



C


1: we dont know anything about the other line but we can find the slope of line l = 2

2: again we dont know the other line's slope but k's is -1/2

Together 2*-1/2= -1

But you could just realize that 1 and 2 are suff together b/c we know the slopes we are going to get a YES OR A NO NOT BOTH. so u could save some time.


how come u get k's = -1/2 in 2 ?


(4,0) and (0,2) --> (0-2)/(4-0) --> -2/4 --> -1/2

Formula for slope is (y1-y2)/(x1-x2)
Manager
Manager
User avatar
Joined: 20 Dec 2004
Posts: 247
Re: DS - if l and k  [#permalink]

Show Tags

New post 02 Feb 2008, 14:41
>> Line K has x-intercept 4 and y-intercept 2.

Its not clear if the x-intercept is going to be a (4,0). All it said is that x-intercept is 4 and y-intercept is 2. Even a coordinate of (-4,0) equals an x-intercept of 4.



So the x coordinates can be (4,0) or (-4,0) and y coordinates can be (0,2) or (0,-2)

So there are two possible lines that are perpendicular and the other 2 are not.

So in my opinion E.

What is the OA ?
_________________

Stay Hungry, Stay Foolish

Manager
Manager
User avatar
Joined: 20 Dec 2004
Posts: 247
Re: DS - if l and k  [#permalink]

Show Tags

New post 02 Feb 2008, 17:44
my mistake if 1) is true then 2) will have a specific set of coordinates.

C is correct... :wall

Need to be more cautious.
_________________

Stay Hungry, Stay Foolish

Manager
Manager
avatar
Joined: 23 Jan 2008
Posts: 108
Re: DS - if l and k  [#permalink]

Show Tags

New post 02 Feb 2008, 21:51
neelesh wrote:
my mistake if 1) is true then 2) will have a specific set of coordinates.

C is correct... :wall

Need to be more cautious.



what do u mean by 2 has to have a specific set of cordinates .. form what i see i agree to your earlier assumption ...when u say line k has 4 as x cordinate and 2 as y cordinate u can very well say that it is a cordinate of the same point (4,2) then u cannot say anything about K's slope as it just passes through one point .. please explain as i still feel it should be E
Manager
Manager
avatar
B
Joined: 02 Nov 2009
Posts: 112
Re: If l and K are lines in xy- plane, is the product of the  [#permalink]

Show Tags

New post 15 Jul 2012, 23:10
Can anyone give a better explanation on this one please

Hovv does K have a slope of -1/2 out of novvhere at all

Please any expert
Intern
Intern
avatar
Joined: 04 Oct 2012
Posts: 12
Concentration: General Management, Human Resources
Schools: Kellogg PT '17
GMAT Date: 02-02-2013
GPA: 3.55
Re: If L and K are lines in xy- plane, is the product of the  [#permalink]

Show Tags

New post 20 Oct 2012, 14:46
read 2) carefully - line K has an x-intercept of 4 (meaning it hits the x axis at 4--- so the point would therefore be 4,0) and y-intercept of 2 (meaning it hits the y axis at 2---so the point would therefore be 0,2). So we now have (4,0) and (0,2) as our two points for line K and we can plug it into our slope formula of y2 - y1/x2 - x1 --> y2 = 2 y1 = 0 x2 - 0 y1 = 4 --> 2-0/0-4 ---> 2/-4 = -1/2.


Hope this helps!
CEO
CEO
User avatar
D
Joined: 12 Sep 2015
Posts: 3021
Location: Canada
Re: If L and K are lines in xy- plane, is the product of the  [#permalink]

Show Tags

New post 30 Apr 2018, 10:23
2
Top Contributor
blog wrote:
If L and K are lines in xy- plane, is the product of the slope of L and K equal to -1?

(1) Line L passes through the origin and the point (1,2).
(2) Line K has x-intercept 4 and y-intercept 2.


IMPORTANT: For geometry and coordinate plane Data Sufficiency questions, we are often checking to see whether the statements "LOCK" a particular line, angle, length, or shape into having just one possible position or measurement. This concept is discussed in much greater detail in the video below.

Target question: Is the product of the slopes of l and k equal to -1?

IMPORTANT: The product of the slopes will equal -1 if the lines are perpendicular to each other (unless the two lines are horizontal and vertical, in which case the product will equal zero). This allows us to REPHRASE the target question as...

REPHRASED target question: Are the two lines perpendicular to each other?

Statement 1: Line l passes through the origin and the point (1, 2)
NOTICE that statement 1 LOCKS line l into ONE AND ONLY ONE line.
That said, we have no information about line k, so we cannot determine whether the two lines are perpendicular to each other.
Since we cannot answer the REPHRASED target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: Line k has x-intercept 4 and y-intercept 2.
NOTICE that statement 1 LOCKS line k into ONE AND ONLY ONE line.
That said, we have no information about line l, so we cannot determine whether the two lines are perpendicular to each other.
Since we cannot answer the REPHRASED target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Statement 1 LOCKS in the shape of line l
Statement 2 LOCKS in the shape of line k
So, we COULD very well determine whether or not the two lines are perpendicular to each other
Since we can answer the REPHRASED target question with certainty, the combined statements are SUFFICIENT

Answer: C

RELATED VIDEO

_________________

Brent Hanneson – GMATPrepNow.com
Image
Sign up for our free Question of the Day emails

GMAT Club Bot
Re: If L and K are lines in xy- plane, is the product of the &nbs [#permalink] 30 Apr 2018, 10:23
Display posts from previous: Sort by

If L and K are lines in xy- plane, is the product of the

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


Copyright

GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.