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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Hi crza,

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

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

VeritasPrepKarishma Bunuel need clarification.

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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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?

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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