It is currently 20 Nov 2017, 14:49

### GMAT Club Daily Prep

#### 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

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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# In the rectangular coordinate system, are the points (r,s)

Author Message
Director
Joined: 10 Feb 2006
Posts: 654

Kudos [?]: 634 [0], given: 0

In the rectangular coordinate system, are the points (r,s) [#permalink]

### Show Tags

01 May 2008, 11:29
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

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

1.r+s =1

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

_________________

GMAT the final frontie!!!.

Kudos [?]: 634 [0], given: 0

Current Student
Joined: 17 Jan 2008
Posts: 585

Kudos [?]: 149 [0], given: 34

Location: Ann Arbor, MI
Schools: Ross '12 (MBA/MS)

### Show Tags

01 May 2008, 11:54
In the rectangular coordinate system, are the points (r,s) and (u,v) equidistance from the origin ?

1.r+s =1

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

(1) Only gives us information about r and s, u and v could be anything. INSUFFICIENT, eliminate AD.
(2) Plug in.
(r,s)=(0,0), (-1,-1), (1,1), (1,0), (0,1).
(u,v)=(1,1), (2,2), (0,0), (0,1), (1,0).
Equidistant from (0,0)? No, no, no, yes, yes.
INSUFFICIENT, eliminate B.

Now go back to (2) and look at all the (r,s) that resulted in (u,v) being equidistant from the origin. All r+s=1 worked, so you know that (1)+(2) is SUFFICIENT, eliminate E.

_________________

Kudos [?]: 149 [0], given: 34

Director
Joined: 10 Sep 2007
Posts: 933

Kudos [?]: 355 [0], given: 0

### Show Tags

01 May 2008, 12:00
Statement 1:
Tells us only above r, and s and nothing about u & v so insufficient. Moreover r, & s can take any value (+ve, -ve, or even 0). Only restriction is their sum should be 1.

Statement 2:
u = 1-r and v=1-s => u+r = 1, v+s = 1
say u = v = 0.9 and r = s = 0.1.
Although equation is satisfied but (0.9, 0.9) is not at same distance from origin as (0.1, 0.1)

Combining both statements:
We have u+r = 1, v+s = 1, and r+s = 1
Add first two equation we have u+v+r+s = 2 => u+v = 1
Only possible way to satisfy this equation is u=v=r=s=0.5

Kudos [?]: 355 [0], given: 0

VP
Joined: 10 Jun 2007
Posts: 1434

Kudos [?]: 370 [0], given: 0

### Show Tags

01 May 2008, 14:00
In the rectangular coordinate system, are the points (r,s) and (u,v) equidistance from the origin ?

1.r+s =1

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

C

Using distance formula, you are looking to answer the question:
Is sqrt(r^2 + s^2) = sqrt(u^2 + v^2) ?
which is same as
Is r^2 + s^2 = u^2 + v^2 ?

(1) INSUFFICIENT, no u or v information

(2) Plug this back into
u^2 + v^2 = 1 - 2r + r^2 + 1 - 2s + s^2 = 2 - 2(r+s) + r^2 + s^2
Only true when r+s = 1
INSUFFICIENT

Using both, r+s=1, the question is answered.
SUFFICIENT

Kudos [?]: 370 [0], given: 0

Re: xy coordinate   [#permalink] 01 May 2008, 14:00
Display posts from previous: Sort by

# In the rectangular coordinate system, are the points (r,s)

Moderator: chetan2u

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.