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Geometry DS Question

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by theachiever » Thu Nov 29, 2012 9:22 pm
What is the length of the median AD to the side BC of a triangle ABC whose centroid lies on the origin?

1.Coordinates of point A is (-4,4)

2.The side BC intercepts the x and y axes at B and C respectively and equation of the line segment BC is y=x-4.
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Source: — Data Sufficiency |
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by eaakbari » Fri Nov 30, 2012 1:12 am
IMO A

Stem: Centroid is at (0,0)
Median AD=?


(I)
A = (-4,4)
We know that a median is divided into the ratio 2:1 at the centroid.

Hence we can use section formula and find the distance between (0,0)& (-4,4). The result will be 2/3 of AD and we can subsequently find AD.

Hence Suff

(II)
BC has equation y = x-4 and has endpoints on the x & y axes.

Equation (0,0) cannot give us a definite line equation. There could be multiple - (x=y, x=-y, x=y^2)

Hence we cannot determine point D on BC and hence cannot determine length of AD. Hence Insuff


IMO A
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by Brent@GMATPrepNow » Fri Nov 30, 2012 9:13 am
I'm pretty sure that the GMAT will not test your knowledge of the terms "centroid" or "median" (as it pertains to a triangle). If a question did involve either term, the GMAT would be sure to include their definitions within the question.
To be 100% certain, you might want to confirm this in the Ask the Test-Maker forum (https://www.beatthegmat.com/ask-the-test-maker-f71.html), but I think this question is out of scope for the GMAT.

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