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In the figure given below, ABCD is a square, and P, Q, R and
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03 Oct 2013, 02:12
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68% (01:42) correct 32% (01:39) wrong based on 286 sessions
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In the figure given below, ABCD is a square, and P, Q, R and S are the midpoints 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
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Re: In the figure given below, ABCD is a square, and P, Q, R and
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03 Oct 2013, 02:27
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 midpoints 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 15607 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. (shaded)/(square)=(1/4)/1=1/4. The ratio for the entire square would be the same. Answer: B.
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Current Student
Joined: 25 Sep 2012
Posts: 263
Location: India
Concentration: Strategy, Marketing
GMAT 1: 660 Q49 V31 GMAT 2: 680 Q48 V34

Re: In the figure given below, ABCD is a square, and P, Q, R and
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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 midpoints 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. (shaded)/(square)=(1/4)/1=1/4. The ratio for the entire square would be the same. Answer: B. 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
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18 Nov 2013, 19:39
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
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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 midpoints 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. (shaded)/(square)=(1/4)/1=1/4. The ratio for the entire square would be the same. Answer: B. 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
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12 Sep 2016, 10:09
b2bt wrote: Attachment: tS6VTJ2.jpg In the figure given below, ABCD is a square, and P, Q, R and S are the midpoints 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 The figure can be seen as four identical squares with identical shaded region and each individual square. And the shaded region is from one end to the mid point of the other corner. This means it's 1/4 of the area of the main square. Since these are identical, the Answer is B) 1/4



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Re: In the figure given below, ABCD is a square, and P, Q, R and
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22 Aug 2018, 07:18
Since the answer choices are quite far from one another, the best way for such graphical problems is approximation. We have got 4 right triangles, which you can easily fit into one of the small (1/4 of original one). Hensce the ratio is 1:4. Time taken 47 sec.
This is I tell you, the guy who is so stubborn as to do algebra when plugin method could perfectly work.




Re: In the figure given below, ABCD is a square, and P, Q, R and &nbs
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22 Aug 2018, 07:18






