Author 
Message 
TAGS:

Hide Tags

Intern
Joined: 23 Nov 2010
Posts: 8

A rectangle is plotted on the standard coordinate plane,
[#permalink]
Show Tags
Updated on: 03 Dec 2010, 11:19
Question Stats:
58% (01:28) correct 42% (01:24) wrong based on 241 sessions
HideShow timer Statistics
A rectangle is plotted on the standard coordinate plane, with vertices at the origin and (12,0). What are the coordinates of the other two vertices? (1) The length of the diagonal is 13 units. (2) The distance between the origin and one of the other vertices is 5 units.
Official Answer and Stats are available only to registered users. Register/ Login.



Intern
Joined: 23 Nov 2010
Posts: 8

Re: DS: Coordinate Plane
[#permalink]
Show Tags
Updated on: 03 Dec 2010, 11:20
***OA INCORRECTLY LISTED AS "A." CORRECT ANSWER IS "E" AS CONFIRMED BELOW.***
I chose E. Does "standard coordinate plane" imply Q1? If not, couldn't the rectangle lie in either Q1 or Q4?
Furthermore, if Q1 is implied, then why is the answer not D?



Math Expert
Joined: 02 Sep 2009
Posts: 59622

Re: DS: Coordinate Plane
[#permalink]
Show Tags
02 Dec 2010, 13:27
JenniferClopton wrote: A rectangle is plotted on the standard coordinate plane, with vertices at the origin and (12,0). What are the coordinates of the other two vertices?
(1) The length of the diagonal is 13 units.
(2) The distance between the origin and one of the other vertices is 5 units. So we have two vertices O(0,0) and B(12,0). First note that OA may be either one of the sides or a diagonal. (1) The length of the diagonal is 13 units > clearly OA is not a diagonal, so it's one of the sides. Now, if we take the length of the other side to be equal to x then we'll have x^2+12^2=13^2 > x=5. But from this we can not get the coordinates of the other vertices. As you correctly noted rectangle can be in I quadrant with the other two vertices at (0, 5) and (12, 5) OR in IV quadrant with the other two vertices at (0, 5) and (12, 5). Not sufficient. (2) The distance between the origin and one of the other vertices is 5 units. Clearly insufficient. (1)+(2) Still two answers are possible: (0, 5) and (12, 5) OR (0, 5) and (12, 5). Not sufficient. Answer: E.
_________________



Intern
Joined: 23 Nov 2010
Posts: 8

Re: DS: Coordinate Plane
[#permalink]
Show Tags
02 Dec 2010, 13:38
OK, while I had not considered the additional possibilities of a rotated position, I concur that the answer is E. Unless I have missed something, this question is wrong? Are we absolutely sure that Q1 is not implied?
Attachments
File comment: Official Question
Untitled2.jpg [ 102.97 KiB  Viewed 4898 times ]



Math Expert
Joined: 02 Sep 2009
Posts: 59622

Re: DS: Coordinate Plane
[#permalink]
Show Tags
02 Dec 2010, 13:43
JenniferClopton wrote: OK, while I had not considered the additional possibilities of a rotated position, I concur that the answer is E.
Unless I have missed something, this question is wrong?
Are we absolutely sure that Q1 is not implied? Yes, I think answer A is wrong. Can you please post OE for it to see where they went wrong?
_________________



Manager
Joined: 30 Aug 2010
Posts: 80
Location: Bangalore, India

Re: DS: Coordinate Plane
[#permalink]
Show Tags
03 Dec 2010, 05:02
JenniferClopton wrote: A rectangle is plotted on the standard coordinate plane, with vertices at the origin and (12,0). What are the coordinates of the other two vertices?
(1) The length of the diagonal is 13 units.
(2) The distance between the origin and one of the other vertices is 5 units. The answr must be "E". Not "A". Please post the correct OA. Here is the simle explanation. Just imagine the rectangle in the coordinate place. You get the answer. No need to use any calculations/values. The below shows the picture with two rectangles, one in red and another in green, which can be drawn for statement given and which have different coordinates except the two given in the question. Attachment:
rectangles.JPG [ 7.93 KiB  Viewed 4829 times ]
Regards, Murali. Kudos?



Intern
Joined: 07 Sep 2010
Posts: 6

Re: DS: Coordinate Plane
[#permalink]
Show Tags
03 Dec 2010, 08:59
even if it is implied the answer shud be D not A becoz 5 cant be the diagonal as one side is already 12 and the diagonal will be greater than both sides.
Cheers, Jaxis.



Intern
Joined: 23 Nov 2010
Posts: 8

Re: DS: Coordinate Plane
[#permalink]
Show Tags
03 Dec 2010, 11:25
Bunuel wrote: Yes, I think answer A is wrong. muralimba wrote: The answr must be "E". Not "A". Please post the correct OA. The answer has been corrected above. Also, for any Grockit subscribers, I have reported the error to the Grockit support team.



Intern
Joined: 04 May 2009
Posts: 41
Location: Astoria, NYC

Re: DS: Coordinate Plane
[#permalink]
Show Tags
07 Dec 2010, 08:17
wow good question i didnt see the other quadrant possibility.



Intern
Joined: 14 Feb 2013
Posts: 19

Re: A rectangle is plotted on the standard coordinate plane,
[#permalink]
Show Tags
22 Jul 2014, 06:44
Bunuel wrote: JenniferClopton wrote: A rectangle is plotted on the standard coordinate plane, with vertices at the origin and (12,0). What are the coordinates of the other two vertices?
(1) The length of the diagonal is 13 units.
(2) The distance between the origin and one of the other vertices is 5 units. So we have two vertices O(0,0) and B(12,0). First note that OA may be either one of the sides or a diagonal. (1) The length of the diagonal is 13 units > clearly OA is not a diagonal, so it's one of the sides. Now, if we take the length of the other side to be equal to x then we'll have x^2+12^2=13^2 > x=5. But from this we can not get the coordinates of the other vertices. As you correctly noted rectangle can be in I quadrant with the other two vertices at (0, 5) and (12, 5) OR in IV quadrant with the other two vertices at (0, 5) and (12, 5). Not sufficient. (2) The distance between the origin and one of the other vertices is 5 units. Clearly insufficient. (1)+(2) Still two answers are possible: (0, 5) and (12, 5) OR (0, 5) and (12, 5). Not sufficient. Answer: E. How can a rectangle have two unequal parallel sides (12 & 13)? beats me



Math Expert
Joined: 02 Sep 2009
Posts: 59622

Re: A rectangle is plotted on the standard coordinate plane,
[#permalink]
Show Tags
22 Jul 2014, 06:48
hamzakb wrote: Bunuel wrote: JenniferClopton wrote: A rectangle is plotted on the standard coordinate plane, with vertices at the origin and (12,0). What are the coordinates of the other two vertices?
(1) The length of the diagonal is 13 units.
(2) The distance between the origin and one of the other vertices is 5 units. So we have two vertices O(0,0) and B(12,0). First note that OA may be either one of the sides or a diagonal. (1) The length of the diagonal is 13 units > clearly OA is not a diagonal, so it's one of the sides. Now, if we take the length of the other side to be equal to x then we'll have x^2+12^2=13^2 > x=5. But from this we can not get the coordinates of the other vertices. As you correctly noted rectangle can be in I quadrant with the other two vertices at (0, 5) and (12, 5) OR in IV quadrant with the other two vertices at (0, 5) and (12, 5). Not sufficient. (2) The distance between the origin and one of the other vertices is 5 units. Clearly insufficient. (1)+(2) Still two answers are possible: (0, 5) and (12, 5) OR (0, 5) and (12, 5). Not sufficient. Answer: E. How can a rectangle have two unequal parallel sides (12 & 13)? beats me It cannot. Where in my solution is written this?
_________________



Intern
Joined: 14 Feb 2013
Posts: 19

Re: A rectangle is plotted on the standard coordinate plane,
[#permalink]
Show Tags
22 Jul 2014, 07:05
(1) The length of the diagonal is 13 units.
(2) The distance between the origin and one of the other vertices is 5 units.[/quote]
So we have two vertices O(0,0) and B(12,0). First note that OA may be either one of the sides or a diagonal.
(1) The length of the diagonal is 13 units > clearly OA is not a diagonal, so it's one of the sides. Now, if we take the length of the other side to be equal to x then we'll have x^2+12^2=13^2 > x=5. But from this we can not get the coordinates of the other vertices. As you correctly noted rectangle can be in I quadrant with the other two vertices at (0, 5) and (12, 5) OR in IV quadrant with the other two vertices at (0, 5) and (12, 5). Not sufficient.
(2) The distance between the origin and one of the other vertices is 5 units. Clearly insufficient.
(1)+(2) Still two answers are possible: (0, 5) and (12, 5) OR (0, 5) and (12, 5). Not sufficient.
Answer: E.[/quote][/quote]
You say clearly OA is not a diagonal, it is one of the side. I think you are mentioning to two sets of parallel lines having length 12 & 13?
Also, how can 13 not be a diagonal, given that it has been explicitly mentioned in the question that it IS a diagonal.



Math Expert
Joined: 02 Sep 2009
Posts: 59622

Re: A rectangle is plotted on the standard coordinate plane,
[#permalink]
Show Tags
22 Jul 2014, 07:31
hamzakb wrote: You say clearly OA is not a diagonal, it is one of the side. I think you are mentioning to two sets of parallel lines having length 12 & 13?
Also, how can 13 not be a diagonal, given that it has been explicitly mentioned in the question that it IS a diagonal. You are not reading the question and the solution carefully. Also, with geometry and coordinate geometry question it's always a good idea to make a sketch: Attachment:
Untitled.png [ 8.01 KiB  Viewed 3623 times ]
OA is NOT the diagonal it's one of the sides, diagonal = 13. Two possible rectangles. Hope it's clear now.
_________________



Intern
Joined: 14 Feb 2013
Posts: 19

Re: A rectangle is plotted on the standard coordinate plane,
[#permalink]
Show Tags
22 Jul 2014, 08:27
Bunuel wrote: hamzakb wrote: You say clearly OA is not a diagonal, it is one of the side. I think you are mentioning to two sets of parallel lines having length 12 & 13?
Also, how can 13 not be a diagonal, given that it has been explicitly mentioned in the question that it IS a diagonal. You are not reading the question and the solution carefully. Also, with geometry and coordinate geometry question it's always a good idea to make a sketch: Attachment: Untitled.png OA is NOT the diagonal it's one of the sides, diagonal = 13. Two possible rectangles. Hope it's clear now. I get it. I didn't understand properly before. Thanks a lot!! Your posts are the most helpful I've found on the net



Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 8245
GPA: 3.82

Re: A rectangle is plotted on the standard coordinate plane,
[#permalink]
Show Tags
22 Oct 2015, 13:27
Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution. A rectangle is plotted on the standard coordinate plane, with vertices at the origin and (12,0). What are the coordinates of the other two vertices? (1) The length of the diagonal is 13 units. (2) The distance between the origin and one of the other vertices is 5 units. There is one variable (b), and 2 equations are given; the answer is likely to be (D). From condition 1, b=5, 5. So this is an insufficient condition as it does not give a unique answer. condition 2, similarly, gives b=5, 5, so this is also insufficient for the same reason. Even if we combine the 2 conditions, b=5,5, so as a whole, they are insufficient, so the answer is going to be (E). For cases where we need 1 more equation, such as original conditions with “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 59 % chance that D is the answer, while A or B has 38% chance and C or E has 3% chance. Since D is most likely to be the answer using 1) and 2) separately according to DS definition. Obviously there may be cases where the answer is A, B, C or E.
_________________
MathRevolution: Finish GMAT Quant Section with 10 minutes to spareThe oneandonly World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only $79 for 1 month Online Course""Free Resources30 day online access & Diagnostic Test""Unlimited Access to over 120 free video lessons  try it yourself"



NonHuman User
Joined: 09 Sep 2013
Posts: 13731

Re: A rectangle is plotted on the standard coordinate plane,
[#permalink]
Show Tags
28 Nov 2019, 07:31
Hello from the GMAT Club BumpBot! Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up  doing my job. I think you may find it valuable (esp those replies with Kudos). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________




Re: A rectangle is plotted on the standard coordinate plane,
[#permalink]
28 Nov 2019, 07:31






