The length of the edging that surrounds circular garden K is

The length of the edging that surrounds circular garden K is 1/2 the length of the edging that surrounds circular garden G. What is the area of garden K (Assume that the edging has negligible width.)

Given that the circumference of garden K is 1/2 of the circumference of garden G, thus the radius of garden is K is 1/2 of the radius of garden G.

We need to find the area of garden K.

(1) The area of G is \(25\pi\) square meters --> we can find the radius of garden G, thus we can find the radius of garden K, hence its area too. Sufficient.

(2) The edging around G is \(10\pi\) meters long --> the circumference of garden G is \(10\pi\). The same here: we can find the radius of garden G, thus we can find the radius of garden K, hence its area too. Sufficient.

Answer: D.
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Both the statements are the same in that they both tell us the radius of G.
So the answer can either be D or E.
Since you can get the radius of G, so its circumference will be 10pi.
The circumference of K is half of that of G, that is 5pi. From this you can find out the radius and hence the area.
+1D

When you can find a radius, then you can calculate both area and circumference of a circle. (D)

The question is very easy and above solutions are excellent. Just want to highlight one part the ratio of two circles circumference = the ratio of their radii, a fact that is very clear to see and saves us time.

Solution:

We are given that the length of edging that surrounds circular garden K is ½ the length of the edging that surrounds circular garden G. Since the gardens are circular, we know that the circumference of garden K is ½ the circumference of circular garden G. We will use the circumference formula C = 2∏r. If we let G = the radius of garden G, and K = the radius of garden K, we can create the following equation.

2∏K = ½(2∏G)

We need to determine the area of garden K, using the area formula A = ∏r^2. Since K = the radius of garden K, we know:

Area of garden K = ∏K^2

Thus, if we can determine the value of K, we can determine the area of garden K.

Statement One Alone:

The area of G is 25∏ square meters.

We can use the information in statement one to determine the value of the radius of garden G.

25∏ = ∏G^2

25 = G^2

√25 = √G^2

5 = G

Since we have the value of G, we can determine the circumference of garden G.

circumference of garden G = 2∏G

circumference = 2∏ x 5

circumference = 10∏

From the given information we also know that:

2∏K = ½(2∏G)

Since 10∏ is the circumference of garden G, we can substitute 10∏ for 2∏G in the equation 2∏K = ½(2∏G). We can now determine a value for K.

2∏K = ½(10∏)

2∏K = 5∏

K = 2.5

Since the radius of garden K is 2.5, we have enough information to determine the area of garden K. Statement one alone is sufficient to answer the question. We can eliminate answer choices B, C, and E.

Statement Two Alone:

The edging around G is 10∏ meters long.

Using the information in statement two, we know that the circumference of garden G is 10∏.

Recall that in statement one, we already determined that the circumference of garden G is 10∏. This is enough information to determine the radius of garden K and hence the area of garden K. Statement two alone is also sufficient to answer the question.

The answer is D.
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Solving DS questions is a really big waste of time

From stem : 2(pi)(rad-k) = 2(pi)(rad-g)/2 : so rad-k = rad-g/2.

radius can't be -ve. So we just have to make sure that we've one +ve rad-g

A) area given. One +ve soln. Enough
2) rad of g can be derived directly.

D

Here, there are 2 circles and each circle relates to each other (circumference of circle K is half of the circumference circle G).
Note:
If you're given any measure (e.g., circumference, radius, diameter, area) of G, you can calculate any measure (e.g., circumference, radius, diameter, area) of K for sure!
So, you can easily find the followings:
circumference of K=\(\frac{1}{2}\) × circumference of G
radius of K=\(\frac{1}{2}\) × radius of G
Area of K=\(\frac{1}{4}\) ×Area of G

You can find radius of G from here, then you can calculate radius of K, then the area of K.
-->Sufficient


You can find radius of G from here, then you can calculate radius of K, then the area of K.
-->Sufficient
So the answer is D
Hope it helps...
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