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19q18

by stubbornp » Sat Oct 18, 2008 10:33 pm
18. In the rectangular coordinate 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
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Source: — Data Sufficiency |
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by Azntycoon » Sun Oct 19, 2008 2:18 pm
See https://www.beatthegmat.com/coordinate-s ... 12489.html for prior response.

However, here's another way to look at it:

From the question, we're basically asked whether:
r^2 + s^2 = u^2 + v^2

(1) Not sufficient. We have 4 variables from the question, but the statement only gives one other equation. We need 4 different equations with the variables above to solve the question.

(2) Not sufficient. Just by looking at the given equations, we will end up with 2 variables (r & s). We still cannot solve the question.

Combined: Sufficient. The equation (with substitution) from Stem #2 and Stem #1 are not the same, and we have 2 different equations for 2 different variables.
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