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

 It is currently 09 Dec 2018, 20:26

### 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 December
PrevNext
SuMoTuWeThFrSa
2526272829301
2345678
9101112131415
16171819202122
23242526272829
303112345
Open Detailed Calendar
• ### Free GMAT Algebra Webinar

December 09, 2018

December 09, 2018

07:00 AM PST

09:00 AM PST

Attend this Free Algebra Webinar and learn how to master Inequalities and Absolute Value problems on GMAT.
• ### Free lesson on number properties

December 10, 2018

December 10, 2018

10:00 PM PST

11:00 PM PST

Practice the one most important Quant section - Integer properties, and rapidly improve your skills.

# In the xy-coordinate system, points (2, 9) and (-1, 0) lie on line k.

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 51035
In the xy-coordinate system, points (2, 9) and (-1, 0) lie on line k.  [#permalink]

### Show Tags

23 Aug 2018, 03:59
00:00

Difficulty:

15% (low)

Question Stats:

83% (01:28) correct 17% (02:02) wrong based on 54 sessions

### HideShow timer Statistics

In the xy-coordinate system, points (2, 9) and (-1, 0) lie on line k. If the point (n, 21) lies on line k, what is the value of n?

A. 6
B. 7
C. 8
D. 9
E. 10

_________________
Director
Status: Learning stage
Joined: 01 Oct 2017
Posts: 931
WE: Supply Chain Management (Energy and Utilities)
Re: In the xy-coordinate system, points (2, 9) and (-1, 0) lie on line k.  [#permalink]

### Show Tags

23 Aug 2018, 04:06
1
Bunuel wrote:
In the xy-coordinate system, points (2, 9) and (-1, 0) lie on line k. If the point (n, 21) lies on line k, what is the value of n?

A. 6
B. 7
C. 8
D. 9
E. 10

Equation of the line passing through points (2, 9) and (-1, 0):

$$y-9=\frac{0-9}{-1-2}*(x-2)$$
Or, y-9=3(x-2), this is the equation of the line k

If the point (n, 21) lies on line k, then this point must satisfy the above equation.
So, 21-9=3n-6
or, 3n-6=12
or, 3n=18
or, n=6

Ans. (A)
_________________

Regards,

PKN

Rise above the storm, you will find the sunshine

Senior SC Moderator
Joined: 22 May 2016
Posts: 2197
In the xy-coordinate system, points (2, 9) and (-1, 0) lie on line k.  [#permalink]

### Show Tags

23 Aug 2018, 19:13
Bunuel wrote:
In the xy-coordinate system, points (2, 9) and (-1, 0) lie on line k. If the point (n, 21) lies on line k, what is the value of n?

A. 6
B. 7
C. 8
D. 9
E. 10

Slope-intercept approach: Find the equation of line $$k$$ in slope-intercept form
$$y=mx+b$$
$$m$$ = slope
$$b$$ = y-intercept

1) Find slope. Use the coordinates of the two given points, (2,9) and (-1,0)

Slope: $$\frac{rise}{run}=\frac{y_2-y_1}{x_2-x_1}=\frac{0-9}{-1-2}=\frac{-9}{-3}=3$$

Plug slope into equation: $$y=3x+b$$

2) Find $$b$$. Plug (x,y) of either given point into equation. Example (-1,0):
$$y=3x+b$$
$$0=3(-1)+b$$
$$0=-3+b$$
$$b=3$$
Plug value of $$b$$ into equation

3) Full equation of line $$k$$ is $$y=3x+3$$. Every point (x, y) [and (n, 21)] on a line must satisfy the equation of the line.

4) Point (n, 21) lies on line $$k$$
$$n =?$$ (n = x-coordinate). Plug in (n, 21)
$$y=3x+3$$
$$21=3n+3$$
$$18=3n$$
$$n=6$$

e-GMAT Representative
Joined: 04 Jan 2015
Posts: 2260
Re: In the xy-coordinate system, points (2, 9) and (-1, 0) lie on line k.  [#permalink]

### Show Tags

23 Aug 2018, 21:00

Solution

Given:
• Points (2, 9) and (-1, 0) lie on line k

To find:
• The value of n such that point (n, 21) also lies on line k.

Approach and Working:

• Points (2, 9) and (-1, 0) lie on line k.
o Hence, slope of line k=$$\frac{{9-0}}{{2- (-1)}}$$= $$\frac{9}{3}$$= 3

• Now, if point (n, 21) also lies on line k then the slope of (n, 21) and(-1, 0) will also be equal to 3.
o $$\frac{{21-0}}{{n+1}}$$= 3
o n=6

Hence, the correct answer is option A.

_________________

Number Properties | Algebra |Quant Workshop

Success Stories
Guillermo's Success Story | Carrie's Success Story

Ace GMAT quant
Articles and Question to reach Q51 | Question of the week

Number Properties – Even Odd | LCM GCD | Statistics-1 | Statistics-2 | Remainders-1 | Remainders-2
Word Problems – Percentage 1 | Percentage 2 | Time and Work 1 | Time and Work 2 | Time, Speed and Distance 1 | Time, Speed and Distance 2
Advanced Topics- Permutation and Combination 1 | Permutation and Combination 2 | Permutation and Combination 3 | Probability
Geometry- Triangles 1 | Triangles 2 | Triangles 3 | Common Mistakes in Geometry
Algebra- Wavy line | Inequalities

Practice Questions
Number Properties 1 | Number Properties 2 | Algebra 1 | Geometry | Prime Numbers | Absolute value equations | Sets

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

Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8649
Location: Pune, India
Re: In the xy-coordinate system, points (2, 9) and (-1, 0) lie on line k.  [#permalink]

### Show Tags

23 Aug 2018, 21:06
Bunuel wrote:
In the xy-coordinate system, points (2, 9) and (-1, 0) lie on line k. If the point (n, 21) lies on line k, what is the value of n?

A. 6
B. 7
C. 8
D. 9
E. 10

Simply use the concept of slope (which many of us think of as Rise/Run) - It is the change in y co-ordinate for a unit change in x co-ordinate)
(2, 9), (-1 , 0) - When x co-ordinate reduces by 3 units, y co-ordinate reduces by 9 units (3 times).
(-1, 0), (n, 21) - So when y co-ordinate increase by 21 units, x co-ordinate will increase by 7 units (1/3).
So n = 6

For more, check: https://www.veritasprep.com/blog/2016/0 ... line-gmat/
_________________

Karishma
Veritas Prep GMAT Instructor

GMAT self-study has never been more personalized or more fun. Try ORION Free!

Re: In the xy-coordinate system, points (2, 9) and (-1, 0) lie on line k. &nbs [#permalink] 23 Aug 2018, 21:06
Display posts from previous: Sort by