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pieces of tile

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pieces of tile

by sairamGmat » Mon Jul 19, 2010 4:19 pm
Image

The figure above shows four pieces of tile that have been glued together to form a square tile ABCD. Is PR=QS?
(1) BQ = CR = DS = AP
(2) The perimeter of ABCD is 16.

OA is A. Not sure how is it A.. Any help?
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by nicolezl » Mon Jul 19, 2010 5:08 pm
(1) Since P, Q, R, S are the same distance away from each of the corners of the square ABCD, they form their own square (not shown) PQRS. PR and QS are the diagonals of that square, so they must be equal.

Sufficient

(2) This doesn't really tell you anything except that each side of the square is 4. Also, PR and QS are 4 root 2, but you wouldn't know that without (1).

Insufficient

So the answer is A.
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by Rahul@gurome » Tue Jul 20, 2010 5:40 am
sairamGmat wrote:Image

The figure above shows four pieces of tile that have been glued together to form a square tile ABCD. Is PR=QS?
(1) BQ = CR = DS = AP
(2) The perimeter of ABCD is 16.

OA is A. Not sure how is it A.. Any help?
(1) Area of trapezium = 0.5 * (base 1 + base 2)*height
The trapeziums ASQB and DRPA will have an equal area. Since they have an equal area and 2 sides are given to be equal, so the 4th side should also be equal. Therefore, PR = QS.
So, (1) is SUFFICIENT.

(2) Perimeter of ABCD does not give any information using which we can show if PR = QS.
So, (2) is NOT SUFFICIENT.

The correct answer is (A).
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by haidgmat » Wed Jul 21, 2010 10:06 am
@Rahul::

Nice approach, however can you tell me if the following approach is correct or not?

Since, BQ=CR=DS=AP and ABCD is a square PB=QC=RD=SA

so the PR must be the same as QS?

Rahul@gurome wrote:
sairamGmat wrote:Image

The figure above shows four pieces of tile that have been glued together to form a square tile ABCD. Is PR=QS?
(1) BQ = CR = DS = AP
(2) The perimeter of ABCD is 16.

OA is A. Not sure how is it A.. Any help?
(1) Area of trapezium = 0.5 * (base 1 + base 2)*height
The trapeziums ASQB and DRPA will have an equal area. Since they have an equal area and 2 sides are given to be equal, so the 4th side should also be equal. Therefore, PR = QS.
So, (1) is SUFFICIENT.

(2) Perimeter of ABCD does not give any information using which we can show if PR = QS.
So, (2) is NOT SUFFICIENT.

The correct answer is (A).
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