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# In the figure given below, ABCD is a square, and P, Q, R and

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Kudos [?]: 113 [3] , given: 242

In the figure given below, ABCD is a square, and P, Q, R and [#permalink]

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03 Oct 2013, 02:12
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Question Stats:

71% (02:45) correct 29% (01:33) wrong based on 167 sessions

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tS6VTJ2.jpg [ 11.04 KiB | Viewed 2719 times ]

In the figure given below, ABCD is a square, and P, Q, R and S are the mid-points of the sides AB, BC, CD and AD respectively. The ratio of the area of the shaded region to the area of the square ABCD is

A. 1/3
B. 1/4
C. 1/5
D. 1/6
E. 1/8
[Reveal] Spoiler: OA
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Kudos [?]: 73460 [1] , given: 9902

Re: In the figure given below, ABCD is a square, and P, Q, R and [#permalink]

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03 Oct 2013, 02:27
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b2bt wrote:
Attachment:
The attachment tS6VTJ2.jpg is no longer available

In the figure given below, ABCD is a square, and P, Q, R and S are the mid-points of the sides AB, BC, CD and AD respectively. The ratio of the area of the shaded region to the area of the square ABCD is

A. 1/3
B. 1/4
C. 1/5
D. 1/6
E. 1/8

Attachment:

Untitled.png [ 30.11 KiB | Viewed 2700 times ]

Consider square APNS and say its side is 1. In this case:

The area of APNS is 1.
MN = 1/2, which means that the area of SMN is 1/2*1/2*1=1/4.

The ratio for the entire square would be the same.

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Senior Manager
Joined: 25 Sep 2012
Posts: 299
Location: India
Concentration: Strategy, Marketing
GMAT 1: 660 Q49 V31
GMAT 2: 680 Q48 V34
Followers: 2

Kudos [?]: 113 [0], given: 242

Re: In the figure given below, ABCD is a square, and P, Q, R and [#permalink]

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03 Oct 2013, 03:08
Bunuel wrote:
b2bt wrote:
Attachment:
tS6VTJ2.jpg

In the figure given below, ABCD is a square, and P, Q, R and S are the mid-points of the sides AB, BC, CD and AD respectively. The ratio of the area of the shaded region to the area of the square ABCD is

A. 1/3
B. 1/4
C. 1/5
D. 1/6
E. 1/8

Attachment:
Untitled.png

Consider square APNS and say its side is 1. In this case:

The area of APNS is 1.
MN = 1/2, which means that the area of SMN is 1/2*1/2*1=1/4.

The ratio for the entire square would be the same.

How did you get MN as half? I solved the same way but assumed it to half...
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Re: In the figure given below, ABCD is a square, and P, Q, R and [#permalink]

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18 Nov 2013, 19:39
1
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BOOKMARKED
APNS is a square. It's side is 1(as assumed by buneul). This means that ABQS is a rectangle with AS=1 and SQ=2. Hence, PN=1. SB and AQ are diagonals of the rectangle. Let them meet at the point M. Draw an imaginary line say XY passing through M and parallel to both AB and SQ. Now observe that PN bisects SQ that is SN=NQ=1. This implies that XY passing through M should also bisect AS, PN and BQ. Therefore, MN=1/2. This property holds good for all rectangles.
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Re: In the figure given below, ABCD is a square, and P, Q, R and [#permalink]

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19 Nov 2013, 04:17
b2bt wrote:
Bunuel wrote:
b2bt wrote:
Attachment:
tS6VTJ2.jpg

In the figure given below, ABCD is a square, and P, Q, R and S are the mid-points of the sides AB, BC, CD and AD respectively. The ratio of the area of the shaded region to the area of the square ABCD is

A. 1/3
B. 1/4
C. 1/5
D. 1/6
E. 1/8

Attachment:
Untitled.png

Consider square APNS and say its side is 1. In this case:

The area of APNS is 1.
MN = 1/2, which means that the area of SMN is 1/2*1/2*1=1/4.

The ratio for the entire square would be the same.

How did you get MN as half? I solved the same way but assumed it to half...

Hello B2bt,

Consider triangle SMN and SBQ

Angles S is common
Angle N is equal to Angle Q and
Angle M is equal to angle B

Since the triangles are similar therefore MN=1/2BQ ie. 1/2
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Re: In the figure given below, ABCD is a square, and P, Q, R and [#permalink]

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09 Jul 2015, 00:01
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Re: In the figure given below, ABCD is a square, and P, Q, R and   [#permalink] 09 Jul 2015, 00:01
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