Coordinate geometry- Data sufficiency

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Coordinate geometry- Data sufficiency

by gmat_thingie » Fri Nov 21, 2014 11:54 pm
What are the coordinates of "S"
a) OS Slope = 1/3
b) ST slope = 1/2

Pls see image in this attachment- Q18
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by [email protected] » Sat Nov 22, 2014 12:22 am
Hi gmat_thingie,

I mentioned this in your other post, but it bears repeating: in a DS prompt, you can't trust any picture you've been given (as far as estimating size or distance is concerned).

Here, we're asked for the Co-ordinates of Point S. From the graph, we know that (0,0) is one co-ordinate on line OS and (5,0) is one co-ordinate on line ST.

Fact 1: The slope of OS = 1/3

Along with the point (0,0), we can now create the equation for line OS:

Y = mX + B
0 = 0/3 + B
B = 0

Line OS is Y = X/3

Unfortunately, this equation has an infinite number of solutions, so we have no way to determine the exact co-ordinate of point S.
Fact 1 is INSUFFICIENT

Fact 2: The slope of ST = 1/2

Along with the point (5,0), we can now create the equation for line ST:

Y = mX + B
0 = 5/2 + B
-2.5 = B

Line ST is Y = X/2 - 2.5

Unfortunately, this equation also has an infinite number of solutions, so we have no way to determine the exact co-ordinate of point S.
Fact 2 is INSUFFICIENT

Combined, we have 2 equations:
Y = X/3
Y = X/2 - 2.5

These 2 equations will criss-cross at just one point: Point S. We COULD determine that co-ordinate, but we don't have to do the math here.
Combined, SUFFICIENT

Final Answer: C

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Rich
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