Rect coordinate system

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gmatblood: Master | Next Rank: 500 Posts; Posts: 489; Joined: Tue Jul 05, 2011 11:10 amFollowed by: 5 members; Thanked: 28 times

by gmatblood » Wed Nov 02, 2011 11:42 am

Rect coordinate system

Detailed explanation required, not just IMO!

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Source: Beat The GMAT — Data Sufficiency | Wed Nov 02, 2011 11:42 am

neelgandham: Community Manager; Posts: 1060; Joined: Fri May 13, 2011 6:46 amFollowed by: 52 members; Location: Utrecht, The Netherlands; Thanked: 318 times

by neelgandham » Wed Nov 02, 2011 2:46 pm

Distance of point (r,s) from the origin (0,0) = Square root((r^2)+(s^2))
Distance of point (u,v) from the origin (0,0) = Square root((u^2)+(v^2))

Question can be rephrased as Is (r^2)+(s^2) = (u^2)+(v^2)

From 1 )r + s = 1 We dont know the values of u and v Insufficient
From 2) u = 1-r, v = 1-s ; Squaring and adding (u^2)+(v^2) = (r^2)+(s^2) + 2 - 2(r + s), Insufficient

From 1 and 2
(u^2)+(v^2) = (r^2)+(s^2) + 2 - 2(r + s) and r+s = 1
=> (u^2)+(v^2) = (r^2)+(s^2) + 2 - 2(1)
=> (u^2)+(v^2) = (r^2)+(s^2)

Sufficient Option C

Anil Gandham
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