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## Identical rectangular tiles

tagged by: Brent@GMATPrepNow

This topic has 2 expert replies and 1 member reply
sidceg Senior | Next Rank: 100 Posts
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#### Identical rectangular tiles

Fri Jul 12, 2013 5:01 am
In the diagram, 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.

OA is D but I got E
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Fri Jul 12, 2013 5:06 am

Whether you are looking at square ABCD or EFGH you can see that the length and height of the outer rectangles must be the same. So horizontally, 3 rectangles and 2 half rectangles equals the vertical height of 4 rectangles. Because the 2 half rectangles equal the one rectangle, they must all be the same.

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Brent@GMATPrepNow GMAT Instructor
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Fri Jul 12, 2013 5:49 am
sidceg wrote:

In the diagram, 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 "shave" 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) = 16L^2
Side EF has length 3L, which means all four sides of square EFGH have length 3L.
So, the area of EFGH = (3L)(3L) = 9L^2
From this, we can conclude that the total area of the rectangles = 16L^2 - 9L^2 = 7L^2
So, the fraction of square ABCD taken up by tiles = (7L^2)/(16L^2) = 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

Cheers,
Brent

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Last edited by Brent@GMATPrepNow on Thu Apr 19, 2018 2:29 pm; edited 1 time in total

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sidceg Senior | Next Rank: 100 Posts
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Fri Jul 12, 2013 5:53 pm
Jim@StratusPrep wrote:

Whether you are looking at square ABCD or EFGH you can see that the length and height of the outer rectangles must be the same. So horizontally, 3 rectangles and 2 half rectangles equals the vertical height of 4 rectangles. Because the 2 half rectangles equal the one rectangle, they must all be the same.
Brent@GMATPrepNow wrote:
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 "shave" 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) = 16L^2
Side EF has length 3L, which means all four sides of square EFGH have length 3L.
So, the area of EFGH = (3L)(3L) = 9L^2
From this, we can conclude that the total area of the rectangles = 16L^2 - 9L^2 = 7L^2
So, the fraction of square ABCD taken up by tiles = (7L^2)/(16L^2) = 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

Cheers,
Brent
Wow! Thank you so much Jim and Brent. I straight away thought without knowing the sides or at least the ratio of the sides of the two squares, the question cannot be solved. But the logic 4L = 3L + 2W did not strike my mind.

Thank you so much once again!

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