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# Just got this data sufficiency on a GMAC practice test and

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Joined: 11 Nov 2007
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Just got this data sufficiency on a GMAC practice test and [#permalink]  11 Nov 2007, 13:33
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Just got this data sufficiency on a GMAC practice test and was wondering if anyone could help me with the explanation.

In the rectangular system are the points (r, s) and (u. v) equidistant from the origin?

1- r + s = 1

2- u= 1-r and v= 1-s

Any help would be greatly appreciated. Thanks
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Joined: 11 Jun 2007
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I think (C)

basically, we have to find if r^2 + s^2 = u^2 + v^2 (distance from (r,s) to origin = distance from (u,v) from origin).

r^2 + s^2 = u^2 + v^2 can be written as:

(r + s)^2 - 2rs = (u + v)^2 - 2uv

we know r + s = 1; u + v = 1;

Therefore, 1 - 2rs = 1 - 2uv.

If we can prove that rs = uv using the three equations:

r + s = 1;
r + u =1;
s + v = 1;

then (C) is the right answer. Let's see if that is the case.

rs = uv --> rs = (1-r)(1-s)
i.e. rs = 1 - r - s + rs;
--> r + s = 1; which is true. Therefore uv = rs.

Hence (C).
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