gmat preparation courses

It is currently Sat Nov 17, 2018 6:25 pm

All times are UTC - 5 hours [ DST ]




Post new topic Reply to topic  [ 4 posts ] 
Author Message
 Post subject: GMAT Coordinate Geometry (Data Sufficiency)
PostPosted: Sat Mar 03, 2012 3:12 pm 
Offline

Joined: Tue Nov 27, 2012 7:29 am
Posts: 12
What are the coordinates of point A in the rectangular coordinate system?
(1) A is 2 units away from (0, 4).
(2) A is 3 units away from (0, 0).

A. Statement (1) BY ITSELF is sufficient to answer the question, but statement (2) by itself is not.
B. Statement (2) BY ITSELF is sufficient to answer the question, but statement (1) by itself is not.
C. Statements (1) and (2) TAKEN TOGETHER are sufficient to answer the question, even though NEITHER statement BY ITSELF is sufficient.
D. Either statement BY ITSELF is sufficient to answer the question.
E. Statements (1) and (2) TAKEN TOGETHER are NOT sufficient to answer the question, meaning that further information would be needed to answer the question.

(E) All the points that lie at some specific distance from a given one are situated on the circle, which center is the given point and the radius is the distance. Therefore each statement by itself defines a circle (infinitively many points). So each statement by itself is NOT sufficient.
If we use the both statements together, we have two circles. Point A belongs to each one of them. Two circles can cross each other in one or two points. (Two circles can also have no common points at all, but it is NOT our case). The distance between the centers, (0, 0) and (0, 4), is √(0² + 4²) = 4. The sum of the radii is 5. If you draw a segment, which connects these two centers, it’s length will be 4. The circle, which center is (0, 0), will cross the segment 3 units away from (0, 0). The circle, which center is (0, 4), will cross the segment 2 units away from (0, 4). It’s clear, that the circles cross each other in exactly TWO different points. So statements (1) and (2) taken together are NOT sufficient to answer the question. The correct answer is E.
----------
How can you tell from the question that you are referring to circles?


Top
 Profile  
 
 Post subject: Re: t.3, qt.37: circles, coordinate geometry, data sufficien
PostPosted: Sat Mar 03, 2012 3:26 pm 
Offline

Joined: Sun May 30, 2010 2:23 am
Posts: 498
Quote:
How can you tell from the question that you are referring to circles?
What is a circle?
It has its center and all points of the circle are on the fixed distance from that center. The distance is called a radius.

So when a statement tells us "A is 2 units away from (0, 4)" it means that A is some point of the circle, which center is (0, 4) and the radius is 2.


Top
 Profile  
 
 Post subject: Re: GMAT Coordinate Geometry (Data Sufficiency)
PostPosted: Tue Sep 25, 2012 5:39 am 
Offline

Joined: Mon Nov 26, 2012 5:39 pm
Posts: 11
Why is the sum of the radii 5? Which radii are you refering to? Thanks.


Top
 Profile  
 
 Post subject: Re: GMAT Coordinate Geometry (Data Sufficiency)
PostPosted: Tue Sep 25, 2012 6:31 am 
Offline

Joined: Sun May 30, 2010 2:23 am
Posts: 498
questioner wrote:
Why is the sum of the radii 5? Which radii are you refering to? Thanks.
Statement (1) defines a circle with the radius 2 and (0, 4) as its center.
Image
So the point A can be any point on the red circle.

Statement (2) defines a circle with the radius 3 and (0, 0) as its center.
Image
So the point A can be any point on the blue circle.

When we combine the two statements we get
Image
So A can be any of the two green points (intersection of the circles). Thus even combined the statements are NOT sufficient.


Attachments:
circle2.gif [5.03 KiB]
Not downloaded yet
circles-combined.gif [7.51 KiB]
Not downloaded yet
circle1.gif [4.86 KiB]
Not downloaded yet
Top
 Profile  
 
Display posts from previous:  Sort by  
Post new topic Reply to topic  [ 4 posts ] 

All times are UTC - 5 hours [ DST ]


Who is online

Users browsing this forum: No registered users and 17 guests


You cannot post new topics in this forum
You cannot reply to topics in this forum
You cannot edit your posts in this forum
You cannot delete your posts in this forum
You cannot post attachments in this forum

Search for:
Jump to:  
cron
Powered by phpBB © 2000, 2002, 2005, 2007 phpBB Group