Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized for You

we will pick new questions that match your level based on your Timer History

Track Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

okay. we want to know whether pts (r,s) and (u,v) are equidistant from the origin (point 0,0) in the coordinate plane.

that means you can have values for r,s and u,v as (-1,0) and (1,0) or (-3,3) and (3,3) or (0,4) and (0,-4) etc etc. you get the picture

1. does r+s=1 tell us anything about point (u,v)? insufficient!

2. rewrite this to u+r=1 and v+s=1

okay few scenarios here

if (r,s) = (0,1) and (u,v) = (1,0) the two coordinates would be equidistant

however if you had values for (r,s) = (-2,-3) and (u,v) = (3,4) then they would NOT be equidistant.
Insufficient

However, they would be sufficient if you had 1 and 2.
no matter how what scenario you run through for both coordinates, with both 1 and 2 you'll have equidistant points.

try it out:

(r,s) = .5, .5 then (u,v) must equal .5 and .5
(r,s) = 0,1 then (u,v) must equal 1,0
(r,s) = 1,0 then (u,v) must equal 0,1
(r,s) = -1,2 then (u,v) must equal 2,-1

I couldn’t help myself but stay impressed. young leader who can now basically speak Chinese and handle things alone (I’m Korean Canadian by the way, so...