nave wrote:
Attachment:
1.jpg
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.
Target question:
What percent of the area of rectangle ABCD is covered by the tiles?Statement 1: ABCD is a square
IMPORTANT: Once we know that ABCD is a square, we also know that EFGH is a square. Notice that if you take square ABCD and "slice" off the same amount (i.e., the width of each rectangle) from the four sides, we get another square (EFGH).
Let L = length of one rectangle.
Side AD has length 4L, which means all four sides of square ABCD have length 4L.
So, the
area of ABCD = (4L)(4L) = 16L²Side EF has length 3L, which means all four sides of square EFGH have length 3L.
So, the
area of EFGH = (3L)(3L) = 9L²From this, we can conclude that the
total area of the rectangles = 16L² - 9L² = 7L²So, the fraction of square ABCD taken up by tiles = (7L²)/(16L²) = 7/16
Since we
could convert 7/16 to a percent, we could determine
the percent of the area of rectangle ABCD is covered by the tiles.
Since we can answer the
target question with certainty, statement 1 is SUFFICIENT
Statement 2: EFGH is a square
Using the same logic that we used above, we know that ABCD must also be a square.
From here, if we follow the same steps as above, we can answer the
target question with certainty.
So statement 2 is SUFFICIENT
Answer = D
Cheers,
Brent