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. 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.
Author 
Message 
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 51035

In the xycoordinate system, points (2, 9) and (1, 0) lie on line k.
[#permalink]
Show Tags
23 Aug 2018, 03:59
Question Stats:
83% (01:28) correct 17% (02:02) wrong based on 54 sessions
HideShow timer Statistics



Director
Status: Learning stage
Joined: 01 Oct 2017
Posts: 931
WE: Supply Chain Management (Energy and Utilities)

Re: In the xycoordinate system, points (2, 9) and (1, 0) lie on line k.
[#permalink]
Show Tags
23 Aug 2018, 04:06
Bunuel wrote: In the xycoordinate 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): \(y9=\frac{09}{12}*(x2)\) Or, y9=3(x2), 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, 219=3n6 or, 3n6=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 xycoordinate system, points (2, 9) and (1, 0) lie on line k.
[#permalink]
Show Tags
23 Aug 2018, 19:13
Bunuel wrote: In the xycoordinate 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 Slopeintercept approach: Find the equation of line \(k\) in slopeintercept form \(y=mx+b\) \(m\) = slope \(b\) = yintercept 1) Find slope. Use the coordinates of the two given points, (2,9) and (1,0) Slope: \(\frac{rise}{run}=\frac{y_2y_1}{x_2x_1}=\frac{09}{12}=\frac{9}{3}=3\)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 = xcoordinate). Plug in (n, 21) \(y=3x+3\) \(21=3n+3\) \(18=3n\) \(n=6\) Answer A



eGMAT Representative
Joined: 04 Jan 2015
Posts: 2260

Re: In the xycoordinate 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=\(\frac{{90}}{{2 (1)}}\)= \(\frac{9}{3}\)= 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 \(\frac{{210}}{{n+1}}\)= 3 o n=6 Hence, the correct answer is option A. Answer: A
_________________
Register for free sessions 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
Must Read Articles Number Properties – Even Odd  LCM GCD  Statistics1  Statistics2  Remainders1  Remainders2 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.egmat.com



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8649
Location: Pune, India

Re: In the xycoordinate system, points (2, 9) and (1, 0) lie on line k.
[#permalink]
Show Tags
23 Aug 2018, 21:06
Bunuel wrote: In the xycoordinate 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 coordinate for a unit change in x coordinate) (2, 9), (1 , 0)  When x coordinate reduces by 3 units, y coordinate reduces by 9 units (3 times). (1, 0), (n, 21)  So when y coordinate increase by 21 units, x coordinate will increase by 7 units (1/3). So n = 6 Answer (A) For more, check: https://www.veritasprep.com/blog/2016/0 ... linegmat/
_________________
Karishma Veritas Prep GMAT Instructor
Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >
GMAT selfstudy has never been more personalized or more fun. Try ORION Free!




Re: In the xycoordinate system, points (2, 9) and (1, 0) lie on line k. &nbs
[#permalink]
23 Aug 2018, 21:06






