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Jack wants to use a circular rug on his rectangular office floor to co

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Jack wants to use a circular rug on his rectangular office floor to cover two small circular stains, each less than \(\frac{π}{100}\) square feet in area and each more than 3 feet from the nearest wall. Can the rug be placed to cover both stains ?

(1) Jack's rug covers an area of 9π square feet.

(2) The centers of the stains are less than 4 feet apart.
[Reveal] Spoiler: OA

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New post 03 Jul 2017, 04:37
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C.

(1) We know that the radius of the rug is 3ft (diameter is 6ft) and the radius of each of the stains is less than 1/10 ft. However we don't know how far the stains are from each other. INSUFFICIENT.

(2) We know that the centers of the stains are less than 4ft apart. Maximum distance between the 2 stains is less than 4 and 2/10 ft. [(2*1/10)+4]. However we do not know the size of the rug if it can completely cover 4 and 2/10 ft. INSUFFICIENT.

With (1) and (2), we know that the diameter of the rug (6ft) can completely cover both stains (max distance is 4 and 2/10 ft). SUFFICIENT.

PS: The information about the stains' location from the wall is unimportant since we do not know the dimensions of the room.

Last edited by crza on 11 Jul 2017, 07:22, edited 1 time in total.

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crza wrote:
C.

(1) We know that the radius of the rug is 3ft (diameter is 6ft) and the radius of each of the stains is 1/10 ft. However we don't know how far the stains are from each other. INSUFFICIENT.

(2) We know that the centers of the stains are less than 4ft apart. Maximum distance between the 2 stains is less than 4 and 2/10 ft. [(2*1/10)+4]. However we do not know the size of the rug if it can completely cover 4 and 2/10 ft. INSUFFICIENT.

With (1) and (2), we know that the diameter of the rug (6ft) can completely cover both stains (max distance is 4 and 2/10 ft). SUFFICIENT.

PS: The information about the stains' location from the wall is unimportant since we do not know the dimensions of the room.



Hi crza,

I think you missed out a keyword - Distance between the 2 stains is less than 4ft but more than 2/10 ft.

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New post 11 Jul 2017, 07:12
ashygoyal wrote:
crza wrote:
C.

(1) We know that the radius of the rug is 3ft (diameter is 6ft) and the radius of each of the stains is 1/10 ft. However we don't know how far the stains are from each other. INSUFFICIENT.

(2) We know that the centers of the stains are less than 4ft apart. Maximum distance between the 2 stains is less than 4 and 2/10 ft. [(2*1/10)+4]. However we do not know the size of the rug if it can completely cover 4 and 2/10 ft. INSUFFICIENT.

With (1) and (2), we know that the diameter of the rug (6ft) can completely cover both stains (max distance is 4 and 2/10 ft). SUFFICIENT.

PS: The information about the stains' location from the wall is unimportant since we do not know the dimensions of the room.



Hi crza,

I think you missed out a keyword - Distance between the 2 stains is less than 4ft but more than 2/10 ft.


Hi ashygoyal,
In my statement above, I computed the maximum possible distance between the 2 stains as follows:
distance between the 2 stains = less than 4 ft
radius of each stain = 1/10 ft
For the purposes of computation, let us suppose the centers of the stains are located 4 ft apart.
Thus, the distance between the 2 stains from 1 end to the other end is 4ft + 1/10 (radius of one stain) + 1/10 (radius of the other stain) = 4 and 2/10 ft.
However, since we are told that the centers are located less than 4 ft apart, the maximum distance must be less than 4 and 2/10 ft.

In this question, we only care about the maximum distance between the stains.
In case you're interested, minimum possible distance between the stains is 4/10. This can be computed by adding the diameter (2/10) of the 2 stains.

Hope my explanation is clear.
Let me know if you have further clarifications! :D

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New post 17 Jul 2017, 15:40
Is this an official question? The information that the stains are 3 ft from the wall seems to be redundant.

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New post 25 Jul 2017, 08:49
More explanation is needed on statement 2. The issue is not clear still now. why the distance is from 4 ft to 2.5 feet? A diagram will be helpful to understand the problem i think

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New post 27 Aug 2017, 20:46
VeritasPrepKarishma Bunuel need clarification.

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New post 29 Aug 2017, 05:10
Hi Bunuel, chetan2u

Could you please provide the diagrammatic explanation of this question.
Thanks in advance.
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New post 29 Aug 2017, 06:48
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Prashant10692 wrote:
Hi Bunuel, chetan2u

Could you please provide the diagrammatic explanation of this question.
Thanks in advance.



Hi..

look at the att fig..
the distance of 3' from the wall does not really effects the answer except when the stains are in the corner in a way that the circular rug does not reach the ends
Solution when statements combined


bigger circle is the circular rug an the smaller circle are the stains...
it is given that stains are pi/100 in square feet, so \(pi*r_1^2=\frac{pi}{100}...r_1=\frac{1}{10}\)
statement II gives the distance between them so the radius of the circular rug required is \(\frac{21}{10}\)
statement I tells us that the area of the circular rug as pi*9 so \(pi*r_2^2=9pi...r_2=3\)..

so the radius required is 21/10 and available is 3...
hence it will cover

C
Attachments

circle1.png
circle1.png [ 10.35 KiB | Viewed 631 times ]


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AbdurRakib wrote:
Jack wants to use a circular rug on his rectangular office floor to cover two small circular stains, each less than \(\frac{π}{100}\) square feet in area and each more than 3 feet from the nearest wall. Can the rug be placed to cover both stains ?

(1) Jack's rug covers an area of 9π square feet.

(2) The centers of the stains are less than 4 feet apart.


Statement One Alone:

Jack's rug covers an area of 9π square feet.

If the area of the rug is 9π square feet, then the radius of the rug is 3 feet, since 3^2 x π = 9π. However, since we don’t know the distance between the centers of the two stains, we can’t determine whether the rug can cover both stains. For example, if the distance between the centers of the two stains is 1 foot, then the rug is big enough to cover them. However, if the distance between the centers of the two stains is 10 feet, then the rug is not big enough to cover them. Statement one alone is not sufficient to answer the question.

Statement Two Alone:

The centers of the stains are less than 4 feet apart.

Without knowing the area of the rug, we can’t determine whether the rug can cover both stains. For example, if the area of the rug is π square feet, then the rug is not big enough to cover them. However, if the area of the rug is 100π square feet, then the rug is big enough to cover them. Statement two alone is not sufficient to answer the question.

Statements One and Two Together:

Using statement one, we know that the radius of the rug is 3 feet, and hence the diameter of the rug is 6 feet. Using statement two, we know that the centers of the stains are less than 4 feet apart. Moreover, we know that each of the stains has an area of less than π/100 square feet, and therefore the radius of each of the stains is less than 1/10 foot. Thus, if we place the rug so that the stains lie on a diameter of the rug, the rug is big enough to cover the stains.

Answer: C
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