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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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New post 19 Feb 2014, 01:17
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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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Re: In the coordinate plane, line k passes through the origin an [#permalink]

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New post 19 Feb 2014, 01:17
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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) --> \(4=2x\) --> \(x=2\);

\(x+y=8\).

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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New post 19 Feb 2014, 03:09
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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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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 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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New post 28 Feb 2015, 19:29
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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

Final Answer:

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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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New post 24 May 2016, 11:59
1
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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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
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Re: In the coordinate plane, line k passes through the origin an [#permalink]

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New post 26 Jul 2017, 23:53
Since the question says that all the points lie on the lie they are col-linear and hence the slope of those points are equal and the slope is given as 2also the points (3,y) and (x,4) are given and if you substitute the values in the equation y=mx+b for both x=3 and y=4 and b being 0 in both cases since the y interscept is 0 we get y=6 and x=2 hence x+y=2+6=8. Hope this helps
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In the coordinate plane, line k passes through the origin an [#permalink]

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New post 06 Mar 2018, 06:19
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





ok here we need to know one very important detail :) for instance it says that slope is \(\frac{1}{2}\) it means change in \(y\) /change in \(x\)

so if slope is 2 which is \(y\) and points (3,y) and (x,4) are on line \(k\),

lets start from (3, y ) that means if \(x\) changes by 3, \(y\) will 2*3 = 6 (i would says its like ratio 1 to 2 where 1 is \(y\) and \(x\) is 2

now lets switch to another point (x,4) ok so if Y is 4, then X will 2

hence 2+6 = 8

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

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New post 08 Mar 2018, 11:31
Bunuel wrote:

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


We are given that line k passes through the origin (or the point (0,0)) and has a slope of 2. Since slope = (change in y)/(change in x), we can create the following equation using the coordinates (0,0) and (3,y):

2 = (y - 0)/(3 - 0)

2 = y/3

y = 6

We can use the slope equation again, this time using the coordinates (0,0) and (x,4):

2 = (4 - 0)/(x - 0)

2 = 4/x

2x = 4

x = 2

Thus, x + y = 6 + 2 = 8.

Answer: C
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Re: In the coordinate plane, line k passes through the origin an   [#permalink] 08 Mar 2018, 11:31
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