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Two squares overlapped

by Abdulla » Thu Jun 25, 2009 3:54 pm
What is the area of the region in which squares ABCD and EFGH overlap?

(1) EF bisects BC.

(2) The distance from point C to point E is and the distance from point C to point F is .

The diagram is attached.

OA is B

Why the first statement is wrong?
Attachments
Picture 3.png
Overlaped squares.pages.zip
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Last edited by Abdulla on Fri Jun 26, 2009 11:33 am, edited 1 time in total.
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Source: — Data Sufficiency |
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by shanmugam.d » Fri Jun 26, 2009 4:22 am
cant open your attachment, can u upload just the jpeg image or word doc?
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by Abdulla » Fri Jun 26, 2009 11:34 am
Thanks shanmugam.d

Check it now
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by ssmiles08 » Fri Jun 26, 2009 1:10 pm
IMO B.

statement 1 is not enough b/c you don't know the actual values of the sides of each squares. Both square could have been equal in length and the result of the overlapping figure would be a square. But if one square was twice the length of the second square, the overlapping area would be that of a rectangle.

2) would produce a 45-45-90 triangle which would make EF = 4.

when you make EF = 4, FG = 4, EG = 4sqrt(2)

you know EC = 2sqrt(2) which is exactly 1/2 of EG.

The overlapping region is a square with a side length of 2, so area is 4.
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by shanmugam.d » Fri Jun 26, 2009 1:29 pm
(1) says that EF bisects BC

- means BC is divided exactly into two halves.
So we can get one side of the small square/ rectangle, but we dont have clue about the other side of the small square/ rectangle

- Not sufficient

(2) says the distance CE = CF =2√2
We know the diagonal of sqaure is xV2, we have x =4, hence diagonal is 4√2.
Thus we can conclude that E is mid point of diagonal AC and C mid point of diagonal HF, and the overlapped portions is a square of side = 2
- Sufficient
answer = (B)
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by Abdulla » Fri Jun 26, 2009 1:38 pm
Guys, I am confused with the wording in the question where it says "What is the area of the region in which squares ABCD and EFGH overlap? " but you guys are saying that it could be square or rectangular ?

Can someone explain ??[/u]
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by ssmiles08 » Fri Jun 26, 2009 1:55 pm
Abdulla wrote:Guys, I am confused with the wording in the question where it says "What is the area of the region in which squares ABCD and EFGH overlap? " but you guys are saying that it could be square or rectangular ?

Can someone explain ??[/u]
OOH i totally missed the part where it gives the side length of 4 for both squares. So they ARE identical to each other. If EF bisects BC, then I would presume that EH bisects DC as well, so it would be sufficient??...

IMO D.

maybe we are missing something? hopefully someone can point it out...Do you have the OE?
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by Abdulla » Fri Jun 26, 2009 5:49 pm
here is the explanations can you explain it :D
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Picture 6.png
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by mehravikas » Fri Jun 26, 2009 8:51 pm
From statement 1, we dont know whether EH bisects DC
Abdulla wrote:here is the explanations can you explain it :D
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by shanmugam.d » Sun Jun 28, 2009 11:11 pm
Hi ABdulla, hope the attachment explains your doubt
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by aj5105 » Sun Jun 28, 2009 11:58 pm
great effort Shanmugam.
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by Abdulla » Mon Jun 29, 2009 1:03 pm
shanmugam.d wrote:Hi ABdulla, hope the attachment explains your doubt
Thanks buddy. It was a great explanation.
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