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# The figure above represents the floor of a square foyer with a circula

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Math Expert
Joined: 02 Sep 2009
Posts: 58320
The figure above represents the floor of a square foyer with a circula  [#permalink]

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09 Dec 2014, 07:33
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Difficulty:

25% (medium)

Question Stats:

73% (01:01) correct 27% (00:45) wrong based on 182 sessions

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Tough and Tricky questions: Geometry.

The figure above represents the floor of a square foyer with a circular rug partially covering the floor and extending to the outer edges of the floor as shown. What is the area of the foyer that is not covered by the rug?

(1) The area of the foyer is 9 square meters.
(2) The area of the rug is 2.25π square meters.

Kudos for a correct solution.

Attachment:

2014-12-09_1832.png [ 2.83 KiB | Viewed 3056 times ]

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Re: The figure above represents the floor of a square foyer with a circula  [#permalink]

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09 Dec 2014, 07:58
2
The figure above represents the floor of a square foyer with a circular rug partially covering the floor and extending to the outer edges of the floor as shown. What is the area of the foyer that is not covered by the rug?

(1) The area of the foyer is 9 square meters.

From Statement 1, we can see that the side of the square foyer measures 3 meters. From this, we can also deduce that the radius of the rug measures 1.5 meters. Therefore, we can figure out the area of the foyer that is not covered by the rug. We don't need to solve, but it would be: 9 meters - 2.25π meters = 1.93 meters

(2) The area of the rug is 2.25π square meters.

From Statement 2, we can deduce that the radius of the rug is 1.5 meters. As in Statement 1, we can see that the side of the square foyer must measure 3 meters. Again, we can use this information to figure out the area of the foyer that is not covered by the rug.

Each statement alone is sufficient to answer the question. Answer is D.
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Re: The figure above represents the floor of a square foyer with a circula  [#permalink]

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09 Dec 2014, 08:22
1
The figure above represents the floor of a square foyer with a circular rug partially covering the floor and extending to the outer edges of the floor as shown. What is the area of the foyer that is not covered by the rug?

(1) The area of the foyer is 9 square meters.
(2) The area of the rug is 2.25π square meters.

Statement 1
The area of the square foyer is 9 square meters => Length of each side of the foyer = 3m
The area of the circular rug = π$${(\frac{3}{2})}^2$$ square meter
Therefore, area of the foyer that is not covered by the rug = 9 - π $${(\frac{3}{2})}^2$$ square meter
The statement is sufficient...........................BCE

Statement 1
The area of the rug is 2.25π square meters => side of the foyer = 1.5*2=3 meter
Or, the area of the foyer is 9 square meter.
Therefore area of the foyer that is not covered by the rug = 9 - 2.25π square meter
The statement is sufficient...........................A D

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Re: The figure above represents the floor of a square foyer with a circula  [#permalink]

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09 Dec 2014, 10:27
1
The figure above represents the floor of a square foyer with a circular rug partially covering the floor and extending to the outer edges of the floor as shown. What is the area of the foyer that is not covered by the rug?

To determine this, we need to take the area of the rug and subtract this from the area of the foyer. All we need is the area of one of the sides of the foyer to determine both areas.

(1) The area of the foyer is 9 square meters. Sufficient--from this we can determine the length of one side of the foyer.
(2) The area of the rug is 2.25π square meters. Sufficient--from this we can determine the radius of the rug, which equals half the length of one side of the foyer.

Choice D
Math Expert
Joined: 02 Sep 2009
Posts: 58320
Re: The figure above represents the floor of a square foyer with a circula  [#permalink]

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26 Dec 2014, 10:26
Bunuel wrote:

Tough and Tricky questions: Geometry.

The figure above represents the floor of a square foyer with a circular rug partially covering the floor and extending to the outer edges of the floor as shown. What is the area of the foyer that is not covered by the rug?

(1) The area of the foyer is 9 square meters.
(2) The area of the rug is 2.25π square meters.

Kudos for a correct solution.

Attachment:
2014-12-09_1832.png

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The figure above represents the floor of a square foyer with a circula  [#permalink]

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18 Dec 2018, 09:25

Project DS Butler: Day 43: Data Sufficiency (DS86)

Bumping for DS Butler project.
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The figure above represents the floor of a square foyer with a circula   [#permalink] 18 Dec 2018, 09:25
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