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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] New post 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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Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 18737
Followers: 3243

Kudos [?]: 22383 [0], given: 2616

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

Answer: C.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

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

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: In the coordinate plane, line k passes through the origin an [#permalink] New post 19 Feb 2014, 02:09
1
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KUDOS
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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Concentration: Finance, General Management
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Kudos [?]: 22 [2] , given: 2

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Re: In the coordinate plane, line k passes through the origin an [#permalink] New post 19 Feb 2014, 20:37
2
This post received
KUDOS
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
Expert Post
Math Expert
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Joined: 02 Sep 2009
Posts: 18737
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Kudos [?]: 22383 [0], given: 2616

Re: In the coordinate plane, line k passes through the origin an [#permalink] New post 22 Feb 2014, 05:00
Expert's post
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.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

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

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Re: In the coordinate plane, line k passes through the origin an   [#permalink] 22 Feb 2014, 05:00
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