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Intern  Joined: 23 Nov 2010
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A rectangle is plotted on the standard coordinate plane,  [#permalink]

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11 00:00

Difficulty:   55% (hard)

Question Stats: 58% (01:28) correct 42% (01:24) wrong based on 241 sessions

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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.

Originally posted by JenniferClopton on 02 Dec 2010, 13:13.
Last edited by JenniferClopton on 03 Dec 2010, 11:19, edited 1 time in total.
Intern  Joined: 23 Nov 2010
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***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?

Originally posted by JenniferClopton on 02 Dec 2010, 13:16.
Last edited by JenniferClopton on 03 Dec 2010, 11:20, edited 2 times in total.
Math Expert V
Joined: 02 Sep 2009
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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.

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Intern  Joined: 23 Nov 2010
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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?
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File comment: Official Question Untitled-2.jpg [ 102.97 KiB | Viewed 4898 times ]

Math Expert V
Joined: 02 Sep 2009
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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?
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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 co-ordinate 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 co-ordinates 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
GMAT 1: 730 Q50 V38 ### Show Tags

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
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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
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Location: Astoria, NYC

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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]

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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.

How can a rectangle have two unequal parallel sides (12 & 13)?

beats me
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Joined: 02 Sep 2009
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Re: A rectangle is plotted on the standard coordinate plane,  [#permalink]

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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.

How can a rectangle have two unequal parallel sides (12 & 13)?

beats me

It cannot. Where in my solution is written this?
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Re: A rectangle is plotted on the standard coordinate plane,  [#permalink]

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(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.

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.
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Re: A rectangle is plotted on the standard coordinate plane,  [#permalink]

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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.
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Re: A rectangle is plotted on the standard coordinate plane,  [#permalink]

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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
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Posts: 8245
GMAT 1: 760 Q51 V42 GPA: 3.82
Re: A rectangle is plotted on the standard coordinate plane,  [#permalink]

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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.
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Re: A rectangle is plotted on the standard coordinate plane,  [#permalink]

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