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In the coordinate plane, line k passes through the origin an

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

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

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New post 19 Feb 2014, 21:37
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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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New post 22 Feb 2014, 06:00
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) --> \(4=2x\) --> \(x=2\);

\(x+y=8\).

Answer: C.
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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

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

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

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New post 28 Feb 2015, 07:50
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

Each week we'll be posting several questions from The Official Guide For GMAT® Quantitative Review, 2ND Edition and then after couple of days we'll provide Official Answer (OA) to them along with a slution.

We'll be glad if you participate in development of this project:
1. Please provide your solutions to the questions;
2. Please vote for the best solutions by pressing Kudos button;
3. Please vote for the questions themselves by pressing Kudos button;
4. Please share your views on difficulty level of the questions, so that we have most precise evaluation.

Thank you!



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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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

Final Answer:
[Reveal] Spoiler:
C


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

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Hello from the GMAT Club BumpBot!

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

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New post 11 May 2016, 09:56
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
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Re: In the coordinate plane, line k passes through the origin an [#permalink]

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New post 24 May 2016, 03:03
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
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Re: In the coordinate plane, line k passes through the origin an [#permalink]

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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?

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

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New post 26 May 2016, 03:21
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, 03:21
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