In the coordinate plane, line k passes through the origin an : GMAT Problem Solving (PS)
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# In the coordinate plane, line k passes through the origin an

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In the coordinate plane, line k passes through the origin an [#permalink]

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19 Feb 2014, 00:17
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The Official Guide For GMAT® Quantitative Review, 2ND Edition

In the coordinate plane, line k passes through the origin and has slope 2. If points (3,y) and (x,4) are on line k, then x+y =

(A) 3.5
(B) 7
(C) 8
(D) 10
(E) 14

Problem Solving
Question: 102
Category: Algebra Simple coordinate geometry
Page: 74
Difficulty: 650

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[Reveal] Spoiler: OA

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19 Feb 2014, 00:17
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SOLUTION

In the coordinate plane, line k passes through the origin and has slope 2. If points (3,y) and (x,4) are on line k, then x+y =

(A) 3.5
(B) 7
(C) 8
(D) 10
(E) 14

Any line which passes through the origin has a form of $$y=mx$$, since $$m=2$$ (the slope of a line), then we have that the equation of our line is $$y=2x$$. Now, if we substitute the coordinates of two points we'll get:

For point (3,y) --> $$y=2*3=6$$;

For point (x,4) --> $$4=2x$$ --> $$x=2$$;

$$x+y=8$$.

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Re: In the coordinate plane, line k passes through the origin an [#permalink]

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19 Feb 2014, 02:09
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Option C.
Origin=(0,0)
Let P1=(3,y)
Equation for line=>y-0=2(3-0)
y=6
Similarly,4-0=2(x-0)
x=2
x+y=8
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19 Feb 2014, 20:37
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Slope of a line which passes through two point (x1,y1) and (x2,y2) is given by-
m=(y2-y1)/(x2-x1)

here m = 2
Here one point is Origin (0,0)
substituting the given values -
2 =(y-0)/(3-0)
y= 6

Similarly, for other point
2 =(4-0)/(x-0)
x =2

So x+y = 8

So correct answer is option C
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Re: In the coordinate plane, line k passes through the origin an [#permalink]

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22 Feb 2014, 05:00
SOLUTION

In the coordinate plane, line k passes through the origin and has slope 2. If points (3,y) and (x,4) are on line k, then x+y =

(A) 3.5
(B) 7
(C) 8
(D) 10
(E) 14

Any line which passes through the origin has a form of $$y=mx$$, since $$m=2$$ (the slope of a line), then we have that the equation of our line is $$y=2x$$. Now, if we substitute the coordinates of two points we'll get:

For point (3,y) --> $$y=2*3=6$$;

For point (x,4) --> $$4=2x$$ --> $$x=2$$;

$$x+y=8$$.

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Re: In the coordinate plane, line k passes through the origin an [#permalink]

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28 Feb 2015, 02:54
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Re: In the coordinate plane, line k passes through the origin an [#permalink]

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28 Feb 2015, 06:50
Bunuel wrote:
The Official Guide For GMAT® Quantitative Review, 2ND Edition

In the coordinate plane, line k passes through the origin and has slope 2. If points (3,y) and (x,4) are on line k, then x+y =

(A) 3.5
(B) 7
(C) 8
(D) 10
(E) 14

Problem Solving
Question: 102
Category: Algebra Simple coordinate geometry
Page: 74
Difficulty: 650

GMAT Club is introducing a new project: The Official Guide For GMAT® Quantitative Review, 2ND Edition - Quantitative Questions Project

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3. Please vote for the questions themselves by pressing Kudos button;
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Similar question : in-the-coordinate-plane-points-x-1-and-10-y-163337.html
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Re: In the coordinate plane, line k passes through the origin an [#permalink]

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28 Feb 2015, 18:29
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Hi All,

This question can be solved with a "brute force" approach, as long as you understand the Graphing vocabulary involved.

We're told that a line passes through the ORIGIN (meaning point 0,0) and has a SLOPE of 2 (meaning the Y-coordinate increases by 2 every time the X-coordiinate increases by 1).

Thus, we can list the first several points (starting at the Origin) without too much trouble:
(0, 0)
(1, 2)
(2, 4)
(3, 6)
(4, 8)
(5, 10)
Etc.

We're told that (3, Y) and (X, 4) are on this line. We're asked for the value of X+Y....

From the list (above), we can see that Y = 6 and that X = 2, so X+Y = 2+6 = 8

[Reveal] Spoiler:
C

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# Special Offer: Save $75 + GMAT Club Tests 60-point improvement guarantee www.empowergmat.com/ ***********************Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!*********************** GMAT Club Legend Joined: 09 Sep 2013 Posts: 13485 Followers: 576 Kudos [?]: 163 [0], given: 0 Re: In the coordinate plane, line k passes through the origin an [#permalink] ### Show Tags 17 Apr 2016, 04:41 Hello from the GMAT Club BumpBot! Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email. _________________ Intern Joined: 10 Aug 2015 Posts: 27 Location: India WE: Consulting (Computer Software) Followers: 0 Kudos [?]: 3 [0], given: 230 In the coordinate plane, line k passes through the origin an [#permalink] ### Show Tags 11 May 2016, 08:56 Bunuel wrote: The Official Guide For GMAT® Quantitative Review, 2ND Edition In the coordinate plane, line k passes through the origin and has slope 2. If points (3,y) and (x,4) are on line k, then x+y = (A) 3.5 (B) 7 (C) 8 (D) 10 (E) 14 So solution of this question is very easy once we know the line passes through origin. When a line passes through origin then its x&y intercept both are '0'. Now equation of the line y=mx+c becomes y=mx=>y=2x. Now plug in the coordinates. Answer is C Manager Joined: 05 Nov 2012 Posts: 57 GMAT 1: 640 Q0 V33 Followers: 0 Kudos [?]: 6 [0], given: 14 Re: In the coordinate plane, line k passes through the origin an [#permalink] ### Show Tags 24 May 2016, 02:03 Bunuel wrote: SOLUTION In the coordinate plane, line k passes through the origin and has slope 2. If points (3,y) and (x,4) are on line k, then x+y = (A) 3.5 (B) 7 (C) 8 (D) 10 (E) 14 Any line which passes through the origin has a form of $$y=mx$$, since $$m=2$$ (the slope of a line), then we have that the equation of our line is $$y=2x$$. Now, if we substitute the coordinates of two points we'll get: For point (3,y) --> $$y=2*3=6$$; For point (x,4) --> $$4=2x$$ --> $$x=2$$; $$x+y=8$$. Answer: C. Hi Bunuel, Why is the answer wrong if I do the question in the following way: y=mx y=2x x+y = x+2x = 3x Now from values given, 4 = 2x x = 2 x+y = 3*2 = 6 EMPOWERgmat Instructor Status: GMAT Assassin/Co-Founder Affiliations: EMPOWERgmat Joined: 19 Dec 2014 Posts: 8306 Location: United States (CA) GMAT 1: 800 Q51 V49 GRE 1: 340 Q170 V170 Followers: 381 Kudos [?]: 2467 [1] , given: 163 Re: In the coordinate plane, line k passes through the origin an [#permalink] ### Show Tags 24 May 2016, 10:59 1 This post received KUDOS Expert's post Hi nishatfarhat87, In your work, you're confusing the VARIABLES X and Y with the X and Y co-ordinates on the line. Try doing your math again, but use these variables instead... Y = 2X (3, B) and (A, 4) are on the line. What is the value of A+B? GMAT assassins aren't born, they're made, Rich _________________ # Rich Cohen Co-Founder & GMAT Assassin # Special Offer: Save$75 + GMAT Club Tests

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Re: In the coordinate plane, line k passes through the origin an [#permalink]

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26 May 2016, 02:21
EMPOWERgmatRichC wrote:
Hi nishatfarhat87,

In your work, you're confusing the VARIABLES X and Y with the X and Y co-ordinates on the line. Try doing your math again, but use these variables instead...

Y = 2X

(3, B) and (A, 4) are on the line. What is the value of A+B?

GMAT assassins aren't born, they're made,
Rich

Got it Rich. Thanks
Re: In the coordinate plane, line k passes through the origin an   [#permalink] 26 May 2016, 02:21
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