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

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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.

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

Is this an official question? The information that the stains are 3 ft from the wall seems to be redundant.

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

VeritasPrepKarishma Bunuel need clarification.

Hi Bunuel, chetan2u

Could you please provide the diagrammatic explanation of this question.
Thanks in advance.
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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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To follow up on some people's comment that the >3 feet distance from the nearest wall is redundant information: No, it's not.

As others have pointed out above, we can conclude from the combined statements (1) and (2) that the rug is large enough to cover both stains. However, the question is if the rug can be placed to cover both stains and to answer this, we must know that it's farther away from the wall than its radius. That is exactly why the 3 feet minimum distance is included in the question.

If the minimum distance was anything less than 3 feet, then the answer would actually be E.

Can you please explain more about highlighted part (with drawing if you can). I seem to have trouble to relate that 3 inch to the question too. why can"t it be for example 2 inches away from the wall?

This is an official DS 287 (OG 2018)
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The gmatquantum explanation might help: https://gmatquantum.com/official-guides/2018-gmat-videos/question-287-data-sufficiency-2018-gmat-official-guide/
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This is a very good question!!

Answer is C.

Posted from my mobile device

Max Radius of each stain is 1/10
Max Diameter of each stain is 1/10 + 1/10 = 2/5
Largest distance between center of stains is 4ft

Max diameter needed to cover is 4+ 1/10 + 1/10 = 21/5 = 4.2
Diameter of rug = 6

6>4.2 there for yes

Max Radius of each stain is 1/10
Max Diameter of each stain is 1/10 + 1/10 = 2/5
Largest distance between center of stains is 4ft

Max diameter needed to cover is 4+ 1/10 + 1/10 = 21/5 = 4.2
Diameter of rug = 6

6>4.2 there for yes

Let radius of each stain = r
\(=> π * r^2 < π/100\)
\(=> r < 0.1\)feet

Statement 1: Area of rug \(= 9π = π * R^2\), where R is the radius of the rug
=> R = 3 feet

However, we do not know how far apart the stains are. If the stains are 2 feet apart, the rug can cover them. However, if the stains are 8 feet apart, the rug cannot cover them - Insufficient

Statement 2: The centers of the stains are less than 4 feet apart.
However, we do not know the radius of the stains. Also, we do not know the size of the rug - Insufficient


Combining:
The stains have radius 0.1 ft; and they are less than 4 feet apart
Thus, the maximum distance between the extreme points of the 2 stains is less than 0.1 + 4 + 0.1 = 4.2 ft
Since the radius of the rug is 3 ft (diameter is 6 ft), the rug can cover the stains.

However, it can cover the stains ONLY IF it were GEOMETRICALLY possible to place the rug over the stains. Since the stains are more than 3 feet away from the walls, there is no problem placing the rug. This is explained in the image below:




Answer C
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1) Don't know how far apart are the 2 stains => Not sufficient

2) Max distance between 2 stains = 4 feet => Since the radius of each circle (1/10) is smaller than the circle formed by the distance between 2 stains, we should consider the bigger area, which would be 4π.
Don't know the area of the circular rug => Not sufficient

1+2) 4π < 9π => Rug will be able to cover the 2 stains => Sufficient

Your sketch shows the stains to be more than 3 feet from top and bottom walls, shouldn't they also be more than 3 feet apart from the left and right walls as well ?