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# In the figure above, if the area of the rectangular region PQRS is 40,

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Math Expert
Joined: 02 Sep 2009
Posts: 49300
In the figure above, if the area of the rectangular region PQRS is 40,  [#permalink]

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11 Oct 2017, 00:59
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Difficulty:

25% (medium)

Question Stats:

85% (01:12) correct 15% (01:47) wrong based on 46 sessions

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In the figure above, if the area of the rectangular region PQRS is 40, and if PT = TS, what is the area of the pentagonal region PQRST?

(A) 15
(B) 20
(C) 25
(D) 30
(E) cannot be determined

Attachment:

2017-10-11_1156_001.png [ 9.81 KiB | Viewed 891 times ]

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Senior Manager
Joined: 05 Dec 2016
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Concentration: Strategy, Finance
GMAT 1: 620 Q46 V29
Re: In the figure above, if the area of the rectangular region PQRS is 40,  [#permalink]

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11 Oct 2017, 01:57

We don't know if T is the centre of PQRS and we don't know the relationship between sides of the triangle.
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Joined: 22 May 2017
Posts: 91
GMAT 1: 580 Q41 V29
GMAT 2: 580 Q43 V27
Re: In the figure above, if the area of the rectangular region PQRS is 40,  [#permalink]

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12 Oct 2017, 07:25
Bunuel wrote:

In the figure above, if the area of the rectangular region PQRS is 40, and if PT = TS, what is the area of the pentagonal region PQRST?

(A) 15
(B) 20
(C) 25
(D) 30
(E) cannot be determined

Attachment:
2017-10-11_1156_001.png

Answer cannot be determined as we dont know the relationship between them.
Target Test Prep Representative
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2835
Re: In the figure above, if the area of the rectangular region PQRS is 40,  [#permalink]

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13 Oct 2017, 09:25
Bunuel wrote:

In the figure above, if the area of the rectangular region PQRS is 40, and if PT = TS, what is the area of the pentagonal region PQRST?

(A) 15
(B) 20
(C) 25
(D) 30
(E) cannot be determined

Attachment:
2017-10-11_1156_001.png

Since we don’t know the length and width of rectangle PSRS (for example, l = 10 and w = 4 OR l = 8 and w = 5), we don’t know the length of PS. Furthermore, since we do not know whether T is the center of the rectangle, there is no way for us to determine the height of triangle PTS, and thus no way to determine the area of the pentagonal region PQRST.

Alternate Explanation:

Figure not drawn to scale means that the point T could be anywhere within the rectangle that satisfies PT = TS; in other words, it could be anywhere on the vertical line that passes through T. If we imagine that point T is located very close to the side PS of the rectangle, the area of the triangle will be very small and the area of the pentagonal region will be close to the area of the rectangle. If, on the other hand, point T is located very close to the side QR of the rectangle, then the area of the triangle will be larger and the area of the pentagonal region will be smaller. Thus, the information provided in the question does not determine the area of the pentagonal region PQRST.

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Re: In the figure above, if the area of the rectangular region PQRS is 40, &nbs [#permalink] 13 Oct 2017, 09:25
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