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Register now and save up to $200 Available with Beat the GMAT members only code • Get 300+ Practice Questions 25 Video lessons and 6 Webinars for FREE Available with Beat the GMAT members only code ## Identical rectangular tiles tagged by: Brent@GMATPrepNow This topic has 2 expert replies and 1 member reply sidceg Senior | Next Rank: 100 Posts Joined 01 Jun 2012 Posted: 89 messages Followed by: 2 members Thanked: 6 times #### Identical rectangular tiles Fri Jul 12, 2013 5:01 am Elapsed Time: 00:00 • Lap #[LAPCOUNT] ([LAPTIME]) 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 Attachments This post contains an attachment. You must be logged in to download/view this file. Please login or register as a user. Need free GMAT or MBA advice from an expert? Register for Beat The GMAT now and post your question in these forums! ### GMAT/MBA Expert Jim@StratusPrep MBA Admissions Consultant Joined 11 Nov 2011 Posted: 2278 messages Followed by: 265 members Thanked: 659 times GMAT Score: 770 Fri Jul 12, 2013 5:06 am The answer here is D. 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. _________________ GMAT Answers provides a world class adaptive learning platform. -- Push button course navigation to simplify planning -- Daily assignments to fit your exam timeline -- Organized review that is tailored based on your abiility -- 1,000s of unique GMAT questions -- 100s of handwritten 'digital flip books' for OG questions -- 100% Free Trial and less than$20 per month after.
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Brent@GMATPrepNow GMAT Instructor
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Fri Jul 12, 2013 5:49 am
sidceg wrote:
ttp://postimg.org/image/xqs2qmxjh/" target="_blank">

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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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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