Geometry

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goyalsau: Legendary Member; Posts: 866; Joined: Mon Aug 02, 2010 6:46 pm; Location: Gwalior, India; Thanked: 31 times

by goyalsau » Wed Nov 17, 2010 10:38 am

HI! guys,
[spoiler]
I don't Understand How the answer is 2:3, in explanation it is given that points are on the same line of slope 3:2, so the points will be on th ratio of 2:3, but origin is also on the line, which has coordinate 0,0
How it that possible then,
[/spoiler]
Please Guys Help,,

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Source: Beat The GMAT — Problem Solving | Wed Nov 17, 2010 10:38 am

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Rahul@gurome: GMAT Instructor; Posts: 1179; Joined: Sun Apr 11, 2010 9:07 pmFollowed by: 88 members; Location: Milpitas, CA; Thanked: 447 times

by Rahul@gurome » Wed Nov 17, 2010 10:58 am

Equation of the line AB is 3x = 2y => x/y = 2/3
Therefore, for any point (x, y) on the line AB, x/y = 2/3
As (p, q) is on AB, p/q = 2/3

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goyalsau: Legendary Member; Posts: 866; Joined: Mon Aug 02, 2010 6:46 pm; Location: Gwalior, India; Thanked: 31 times

by goyalsau » Fri Nov 19, 2010 7:39 am

Rahul@gurome wrote:Equation of the line AB is 3x = 2y => x/y = 2/3
Therefore, for any point (x, y) on the line AB, x/y = 2/3
As (p, q) is on AB, p/q = 2/3

I am not able to understand one thing, this line will also pass from the origin ( 0 , 0 )

If p , q are at origin then........

Saurabh Goyal
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Rahul@gurome: GMAT Instructor; Posts: 1179; Joined: Sun Apr 11, 2010 9:07 pmFollowed by: 88 members; Location: Milpitas, CA; Thanked: 447 times

by Rahul@gurome » Fri Nov 19, 2010 7:50 am

goyalsau wrote:
Rahul@gurome wrote:Equation of the line AB is 3x = 2y => x/y = 2/3
Therefore, for any point (x, y) on the line AB, x/y = 2/3
As (p, q) is on AB, p/q = 2/3
I am not able to understand one thing, this line will also pass from the origin ( 0 , 0 )

If p , q are at origin then........

As the point shown in the figure suggests that point B is not origin, the answer remains same as I discussed. But I should have also mentioned that for any point (x, y) on the line AB (except (0, 0)), x/y = 2/3.

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MAAJ: Master | Next Rank: 500 Posts; Posts: 243; Joined: Sun Jul 12, 2009 7:12 amFollowed by: 2 members; Location: Dominican Republic; Thanked: 31 times; GMAT Score:480

by MAAJ » Fri Nov 19, 2010 11:08 am

My noob way to solve this:

m = (y2-y1)/(x2-x1)
m = (3-0)/(2-0)
m = 3/2

so... if x=0 and y=0

y = 3/2x + b
0 = 3/2(0) + b
0 = 0 + b
0 = b

so... if "b" is always 0

y = 3/2x

so... if x=p and y=q

q=3/2p

then p/q:

p/q
p/(3/2p)
2/3

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