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# On a graph the four corners of a certain quadrilateral

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Intern
Joined: 18 Dec 2012
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On a graph the four corners of a certain quadrilateral [#permalink]

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04 Jan 2013, 03:06
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On a graph the four corners of a certain quadrilateral are (a,5), (b,5), (a,0) and (b,0). If a + c = 12, a < b and both a and b are positive values then what is the area of the quadrilateral?

(1) b + c = 6
(2) The quadrilateral is a rectangle.
[Reveal] Spoiler: OA

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Re: On a graph the four corners of a certain quadrilateral [#permalink]

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04 Jan 2013, 04:41
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Expert's post
trex16864 wrote:
On a graph the four corners of a certain quadrilateral are (a,5), (b,5), (a,0) and (b,0). If a + c = 12, a < b and both a and b are positive values then what is the area of the quadrilateral?

(1) b + c = 6
(2) The quadrilateral is a rectangle.

There is a problem with this question. We are given that a + c = 12 and (1) says that b + c = 6, thus a = b + 6, which implies that a > b. But the stem says that a < b. I guess it should be a > b instead of a < b.

In this case the question would be:
On a graph the four corners of a certain quadrilateral are (a,5), (b,5), (a,0) and (b,0). If a + c = 12, a > b and both a and b are positive values then what is the area of the quadrilateral?

Look at the diagram below:
Attachment:

Quadrilateral.PNG [ 9.43 KiB | Viewed 3144 times ]
As we can see given quadrilateral is a rectangle and its area = 5*(a-b).

(1) b + c = 6. Since a + c = 12 and b + c = 6, then a - b = 6. Area = 5*6=30. Sufficient.

(2) The quadrilateral is a rectangle. We already know that. Not sufficient.

Hope it's clear.
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Re: On a graph the four corners of a certain quadrilateral [#permalink]

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04 Jan 2013, 03:54
My solution:

Given the information in the question we can already conclude, that the quadriliteral is a rectangle with a width of 5. We need to figure out the length of the rectangle in order to find the area.

(1) with
I) $$a + c = 12$$
II) $$b + c = 6$$

we can I) - II) => $$(a-b) = 6$$

Length = Distance [(a;5) (b;5)] = Distance [(a;0) (b;0)] =
= SQR [ $$(a-b)^2 + (5-5)^2$$ ]
= SQR [ $$6^2 + 0^2$$ ]

= 6

=> $$Area = 6 * 5 = 30$$ sufficient

(2) We already know that we have a rectangle. The statement gives us no further information about the length. Not sufficent

Hence A

Last edited by trex16864 on 04 Jan 2013, 05:04, edited 2 times in total.

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Re: On a graph the four corners of a certain quadrilateral [#permalink]

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01 Jun 2013, 01:16
Bunuel wrote:
trex16864 wrote:
On a graph the four corners of a certain quadrilateral are (a,5), (b,5), (a,0) and (b,0). If a + c = 12, a < b and both a and b are positive values then what is the area of the quadrilateral?

(1) b + c = 6
(2) The quadrilateral is a rectangle.

There is a problem with this question. We are given that a + c = 12 and (1) says that b + c = 6, thus a = b + 6, which implies that a > b. But the stem says that a < b. I guess it should be a > b instead of a < b.

In this case the question would be:
On a graph the four corners of a certain quadrilateral are (a,5), (b,5), (a,0) and (b,0). If a + c = 12, a > b and both a and b are positive values then what is the area of the quadrilateral?

Look at the diagram below:
Attachment:
As we can see given quadrilateral is a rectangle and its area = 5*(a-b).

(1) b + c = 6. Since a + c = 12 and b + c = 6, then a - b = 6. Area = 5*6=30. Sufficient.

(2) The quadrilateral is a rectangle. We already know that. Not sufficient.

Hope it's clear.

Hi,

Sorry to re-open the thread. But Can you please explain how does the question stem tells us that it is a rectangle?

Thank you

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Re: On a graph the four corners of a certain quadrilateral [#permalink]

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01 Jun 2013, 04:17
Genfi wrote:
Bunuel wrote:
trex16864 wrote:
On a graph the four corners of a certain quadrilateral are (a,5), (b,5), (a,0) and (b,0). If a + c = 12, a < b and both a and b are positive values then what is the area of the quadrilateral?

(1) b + c = 6
(2) The quadrilateral is a rectangle.

There is a problem with this question. We are given that a + c = 12 and (1) says that b + c = 6, thus a = b + 6, which implies that a > b. But the stem says that a < b. I guess it should be a > b instead of a < b.

In this case the question would be:
On a graph the four corners of a certain quadrilateral are (a,5), (b,5), (a,0) and (b,0). If a + c = 12, a > b and both a and b are positive values then what is the area of the quadrilateral?

Look at the diagram below:
Attachment:
As we can see given quadrilateral is a rectangle and its area = 5*(a-b).

(1) b + c = 6. Since a + c = 12 and b + c = 6, then a - b = 6. Area = 5*6=30. Sufficient.

(2) The quadrilateral is a rectangle. We already know that. Not sufficient.

Hope it's clear.

Hi,

Sorry to re-open the thread. But Can you please explain how does the question stem tells us that it is a rectangle?

Thank you

Mark (a,5), (b,5), (a,0) and (b,0) on the plane and you'll see that you'll get a rectangle for any values of a and b (a>b).
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Re: On a graph the four corners of a certain quadrilateral [#permalink]

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01 Jun 2013, 16:27
The b > a threw me off...

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Re: On a graph the four corners of a certain quadrilateral [#permalink]

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17 May 2016, 06:13
Bunuel wrote:
trex16864 wrote:
On a graph the four corners of a certain quadrilateral are (a,5), (b,5), (a,0) and (b,0). If a + c = 12, a < b and both a and b are positive values then what is the area of the quadrilateral?

(1) b + c = 6
(2) The quadrilateral is a rectangle.

There is a problem with this question. We are given that a + c = 12 and (1) says that b + c = 6, thus a = b + 6, which implies that a > b. But the stem says that a < b. I guess it should be a > b instead of a < b.

In this case the question would be:
On a graph the four corners of a certain quadrilateral are (a,5), (b,5), (a,0) and (b,0). If a + c = 12, a > b and both a and b are positive values then what is the area of the quadrilateral?

Look at the diagram below:
Attachment:
As we can see given quadrilateral is a rectangle and its area = 5*(a-b).

(1) b + c = 6. Since a + c = 12 and b + c = 6, then a - b = 6. Area = 5*6=30. Sufficient.

(2) The quadrilateral is a rectangle. We already know that. Not sufficient.

Hope it's clear.

Thanks Bunel, I couldn't agree more, due to this a<b issue, I was getting the error as "negative" and marked E instead, I would my answer had correct now - not gonna spoil my metrics for an incorrect question, Author - Please edit and correct the question, it's misleading.
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Re: On a graph the four corners of a certain quadrilateral [#permalink]

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06 Jun 2016, 11:01
Same here, the part on a<b made me choose E. Could anyone please fix this issue?
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Re: On a graph the four corners of a certain quadrilateral   [#permalink] 06 Jun 2016, 11:01
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# On a graph the four corners of a certain quadrilateral

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