It is currently 19 Apr 2018, 21:44

### 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

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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# In the xy-plane, l and m are two lines. (3, 4) is a point only on

Author Message
TAGS:

### Hide Tags

Intern
Joined: 24 Mar 2018
Posts: 8
In the xy-plane, l and m are two lines. (3, 4) is a point only on [#permalink]

### Show Tags

11 Apr 2018, 10:37
3
This post was
BOOKMARKED
00:00

Difficulty:

(N/A)

Question Stats:

12% (00:00) correct 88% (01:26) wrong based on 17 sessions

### HideShow timer Statistics

In the xy-plane, l and m are two lines. (3, 4) is a point only on one among l and m and (4, 5) lies only on the other. Are lines l and m perpendicular?

(1) The slope of line l is −1.
(2) They intersect at (2, 1).
[Reveal] Spoiler: OA
Manager
Joined: 22 Feb 2018
Posts: 73
In the xy-plane, l and m are two lines. (3, 4) is a point only on [#permalink]

### Show Tags

12 Apr 2018, 04:20
1
KUDOS
hetmavani wrote:
In the xy-plane, l and m are two lines. (3, 4) is a point only on one among l and m and (4, 5) lies only on the other. Are lines l and m perpendicular?

(1) The slope of line l is −1.
(2) They intersect at (2, 1).

OA is D.

as per question , Points are (3,4) , (4,5). Only one point of these lie on line l, other has be on m.

Statement 1 : The slope of line l is −1.

Case 1
if (3,4) falls on line l ,then equation of line l will be

$$\frac{(y-4)}{(x-3)}$$=-1
y=-x+7

Assume that line m passing through (4,5) is perpeniducular to line l
As product of slope of two non vertical perpendicular line is -1.
Slope of line m would be 1
$$\frac{(y-5)}{(x-4)}$$=1
y=x+1
Now the point of interesection of line l and m would come out be (3,4).
As per question (3,4) should not lie on line m.
so Slope of m cannot ever be -1.
This tell us that l cannot be perpendicular to m.

Case 2
if (4,5) falls on line l ,then equation of line l will be

$$\frac{(y-5)}{(x-4)}$$=-1
y=−x+9

Assume that line m passing through (3,4) is perpeniducular to line l
As product of slope of two non vertical perpendicular line is -1.
Slope of line m would be 1
$$\frac{(y-4)}{(x-3)}$$=1
y=x+1
Now the point of interesection of line l and m would come out be (4,5).
As per question (4,5) should not lie on line m.
so Slope of m cannot ever be -1.
This tell us that l cannot be perpendicular to m.

So Statement 1 alone is sufficient to give a definite answer(i.e No) for question: Are lines l and m perpendicular?.

Statement 2 : line l and m interesect at (2,1)
Now we have got two points on each line , so each of these two line can be defined.
We do not need nomenclature l,m.To avoid confusion,We can just name them as line 1 and line 2
Line 1 passing through point (3,4) and (2,1)

$$\frac{(y−4)}{(x−3)}$$=$$\frac{(1-4)}{(2-3)}$$
y=3x−5

Line 2 passing through point (4,5) and (2,1)

$$\frac{(y−5)}{(x−4)}$$=$$\frac{(1-5)}{(2-4)}$$
y=2x−3

For two non vertical line to be perpendicular , product of their slope should be -1.
In case of line 1 and line 2 , product of their slope is 3∗2= 6
Hence , we are getting a definite answer(i.e No) for question: Are lines l and m perpendicular?
Statement 2 alone is sufficient

As Statement 1 and Statement 2 are both alone sufficient , OA should be D
_________________

Good, good Let the kudos flow through you

SVP
Joined: 08 Jul 2010
Posts: 2062
Location: India
GMAT: INSIGHT
WE: Education (Education)
In the xy-plane, l and m are two lines. (3, 4) is a point only on [#permalink]

### Show Tags

12 Apr 2018, 05:10
1
KUDOS
Expert's post
hetmavani wrote:
In the xy-plane, l and m are two lines. (3, 4) is a point only on one among l and m and (4, 5) lies only on the other. Are lines l and m perpendicular?

(1) The slope of line l is −1.
(2) They intersect at (2, 1).

A very Good CONCEPT but a disqualified question as per GMAT standard as statement 1 and 2 are contradictory because using statement 2 none of the lines gives slope -1 which is given in statement 1.

Question : Are lines l and m perpendicular lines?

CONCEPT
: The two lines are perpendicular if the product opf their slopes = -1

Statement 1: The slope of line l is −1

For the lines l and m to be perpendicular the slope of line m should be 1 as per the information in statement 1

But the slope of points (3, 4) and (4, 5) is 1 and both points do NOT lie on any one line
i.e. Slope of line m can't be 1
i.e. Line m and l are definitely NOT Perpendicular lines

SUFFICIENT

Statement 2: They intersect at (2, 1)
Now we have two points on each of the line m and l so we can find the slope of each line and find out if the lines are perpendicular or NOT hence
SUFFICIENT

P.S. We need not calculate everything when we can realize that using the given information the answer has to be unique.

_________________

Prosper!!!
GMATinsight
Bhoopendra Singh and Dr.Sushma Jha
e-mail: info@GMATinsight.com I Call us : +91-9999687183 / 9891333772
Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi
http://www.GMATinsight.com/testimonials.html

22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION

In the xy-plane, l and m are two lines. (3, 4) is a point only on   [#permalink] 12 Apr 2018, 05:10
Display posts from previous: Sort by