Data Sufficiency

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?

cant open your attachment, can u upload just the jpeg image or word doc?

Thanks shanmugam.d

Check it now

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.

(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)

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]

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?

here is the explanations can you explain it

From statement 1, we dont know whether EH bisects DC

Abdulla wrote:here is the explanations can you explain it

Hi ABdulla, hope the attachment explains your doubt

great effort Shanmugam.

shanmugam.d wrote:Hi ABdulla, hope the attachment explains your doubt

Thanks buddy. It was a great explanation.