OG Co-Geometry

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GmatKiss: Legendary Member; Posts: 2789; Joined: Tue Jul 26, 2011 12:19 amFollowed by: 43 members; Location: Chennai, India; Thanked: 206 times; GMAT Score:640

by GmatKiss » Sun Oct 30, 2011 1:52 pm

In the xy-coordinate system, if (a,b) and (a + 3,b + k)
are two points on the line defined by the equation
x = 3y - 7, then k =

9
3
7/3
1
1/3

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Source: Beat The GMAT — Problem Solving | Sun Oct 30, 2011 1:52 pm

GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Sun Oct 30, 2011 2:04 pm

GmatKiss wrote:In the xy-coordinate system, if (a,b) and (a + 3,b + k)
are two points on the line defined by the equation
x = 3y - 7, then k =

9
3
7/3
1
1/3

The equation of the line rephrased as y = mx+b:
3y-7 = x
3y = x+7
y = (1/3)x + 7/3.

Slope = 1/3.
Since (a,b) and (a+3,b+k) are two points on the line, and slope = (change in y/change in x), we get:
(b+k-b)/(a+3-a) = 1/3.
k/3 = 1/3.
k=1.

The correct answer is D.

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shankar.ashwin: Legendary Member; Posts: 966; Joined: Sat Jan 02, 2010 8:06 amFollowed by: 21 members; Thanked: 230 times

by shankar.ashwin » Sun Oct 30, 2011 4:38 pm

An alternate method;

Eq of the line is x=3y-7. Substitute any(x,y) which satisfies this equation. Lets assume (2,3). Now (a,b)=(2,3)

We need to find k for (2+3, 3+k) or (5,3+k)

5=3(3+k) - 7
3+k=4
k=1 D

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GmatKiss: Legendary Member; Posts: 2789; Joined: Tue Jul 26, 2011 12:19 amFollowed by: 43 members; Location: Chennai, India; Thanked: 206 times; GMAT Score:640

by GmatKiss » Mon Oct 31, 2011 12:35 am

Thanks a lot Mitch

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Gokhra: Junior | Next Rank: 30 Posts; Posts: 16; Joined: Sat Sep 17, 2011 8:23 amFollowed by: 1 member; Thanked: 1 times

by Gokhra » Mon Oct 31, 2011 1:59 am

Just to share my method of solving:

The equation is x = 3y - some constant

As soon as I see it, I think "every time you increase y by 1, x increases by 3." The question asks exactly that, "How much do you increase y by to increase x by 3?"

Basically, instead of trying to solve the equations for variables, just restating the question helped me get to the answer very quickly.

Hope this will be helpful to someone!

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vaibhavgupta: Master | Next Rank: 500 Posts; Posts: 416; Joined: Tue Aug 30, 2011 2:18 pmFollowed by: 9 members; Location: Delhi, India; Thanked: 13 times

by vaibhavgupta » Mon Oct 31, 2011 5:24 am

GmatKiss wrote:In the xy-coordinate system, if (a,b) and (a + 3,b + k)
are two points on the line defined by the equation
x = 3y - 7, then k =

9
3
7/3
1
1/3

D it is!

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