pareekbharat86 wrote:
In the diagram above, the fourteen rectangular tiles are all identical. What percent of the area of rectangle ABCD is covered by the tiles?
(1) ABCD is a square.
(2) EFGH is a square.
Statement 1: ABCD is a square
For ABCD to be a square, the length of each tile must be twice the width, as the cases below will illustrate.
Case 1: Each rectangle is 2 feet by 1 foot
Area of ABCD = 8*8 = 64.
Area of the 14 tiles = 14*2*1 = 28.
Resulting ratio:
(tile area)/(total area) = 28/64 = 7/16.
Case 2: Each rectangle is 4 feet by 2 feet
Area of ABCD = 16*16 = 256.
Area of the 14 tiles = 14*4*2 = 112.
Resulting ratio:
(tile area)/(total area) = 112/256 = 56/128 = 7/16.
The resulting ratio is THE SAME in each case.
The implication is that -- in EVERY case -- the following ratio will be yielded:
(tile area)/(total area) = 7/16.
SUFFICIENT.
Statement 2: EFGH is a square
For EFGH to be a square, ABCD must also be a square.
Thus, statement 2 implies the same information as statement 1.
Since statement 1 is sufficient, statement 2 also is SUFFICIENT.
The correct answer is
D.
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