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

It is currently 25 Jun 2018, 07:07

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

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

In the coordinate plane, Line M travels through points (9,10), (0,4),

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

Hide Tags

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 46302
In the coordinate plane, Line M travels through points (9,10), (0,4), [#permalink]

Show Tags

New post 29 May 2018, 22:34
00:00
A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

84% (01:03) correct 16% (01:01) wrong based on 57 sessions

HideShow timer Statistics

Manager
Manager
User avatar
S
Joined: 28 Nov 2017
Posts: 145
Location: Uzbekistan
Premium Member
Re: In the coordinate plane, Line M travels through points (9,10), (0,4), [#permalink]

Show Tags

New post 29 May 2018, 22:57
1
Bunuel wrote:
In the coordinate plane, Line M travels through points (9,10), (0,4), and (−9,n). What is the value of n?

A. −10

B. −6

C. −10/3

D. −2

E. −4/3


Line \(M\) can be expressed as
\(y=kx+b\)

We have the system of equations
\(9k+b=10\)
\(0+b=4\)

So, \(b=4\), \(k=\frac{2}{3}\) and \(y=\frac{2}{3}x+4\)

Now, let's check \((−9,n)\) with \(y=\frac{2}{3}x+4\).
\(n=\frac{2}{3}*(-9)+4=-2\)

Answer: D
_________________

Kindest Regards!
Tulkin.

Expert Post
2 KUDOS received
e-GMAT Representative
User avatar
G
Joined: 04 Jan 2015
Posts: 1596
Re: In the coordinate plane, Line M travels through points (9,10), (0,4), [#permalink]

Show Tags

New post 29 May 2018, 23:27
2
1

Solution



Given:
    • In the coordinate plane, Line M travels through points (9, 10), (0, 4), and (-9, n)

To find:
    • The value of n

Approach and Working:
As the points are colinear, the slope calculated by taking any points at a time will be the same always.
Therefore, we can write
    • \(\frac{(4-10)}{(0-9)} = \frac{(n-4)}{(-9-0)}\)
    Or, \(\frac{-6}{-9} = \frac{(n – 4)}{-9}\)
    Or, n = -2

Hence, the correct answer is option D.

Answer: D
_________________












| '4 out of Top 5' Instructors on gmatclub | 70 point improvement guarantee | www.e-gmat.com

SC Moderator
avatar
D
Joined: 22 May 2016
Posts: 1766
Premium Member CAT Tests
In the coordinate plane, Line M travels through points (9,10), (0,4), [#permalink]

Show Tags

New post 31 May 2018, 14:16
Bunuel wrote:
In the coordinate plane, Line M travels through points (9,10), (0,4), and (−9,n). What is the value of n?

A. −10

B. −6

C. −10/3

D. −2

E. −4/3

We need an equation for the line.
Any point on the line makes the equation true.
We have point (-9,n). x-coordinate is -9.
Plug -9 into line's equation. Result is the y-coordinate for that point, here called \(n\).

Slope intercept form is easy to use, thus:
\(y=mx+b\) in which \(m\) = slope and \(b\) = y-intercept

y-intercept: When \(x=0\), \(y=?\)
From (0,4), y-intercept = \(+ 4 = b\)
So far we have: \(y=mx+4\)

Use given points (9,10) and (0,4). Find slope

Slope = \(m\)
Slope=\(\frac{rise}{run}=\frac{y_2-y_1}{x_2-x_1}=\frac{10-4}{9-0}=\frac{6}{9}=\frac{2}{3}=m\)

Equation of the line
We have: \(y=\frac{2}{3}x+4\)

Coordinates
\((-9,n)\): what is \(n\)?
Plug \(x=-9\) into equation
For THIS point, y-coordinate \(=n\)
\(y=((\frac{2}{3}*-9)+4)=(-6+4)=-2=n\)

\(n = -2\)

Answer D
_________________

In the depths of winter, I finally learned
that within me there lay an invincible summer.

-- Albert Camus, "Return to Tipasa"

Expert Post
Target Test Prep Representative
User avatar
G
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2570
Re: In the coordinate plane, Line M travels through points (9,10), (0,4), [#permalink]

Show Tags

New post 31 May 2018, 16:15
Bunuel wrote:
In the coordinate plane, Line M travels through points (9,10), (0,4), and (−9,n). What is the value of n?

A. −10

B. −6

C. −10/3

D. −2

E. −4/3


Since line M travels though all the given points, the slopes between any pairs of points have to be the same; thus:

(4 - 10)/(0 - 9) = (n - 4)/(-9 - 0)

-6/-9 = (n - 4)/-9

-6 = n - 4

-2 = n

Answer: D
_________________

Jeffery Miller
Head of GMAT Instruction

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Re: In the coordinate plane, Line M travels through points (9,10), (0,4),   [#permalink] 31 May 2018, 16:15
Display posts from previous: Sort by

In the coordinate plane, Line M travels through points (9,10), (0,4),

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


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®.