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# What is the area of the innermost circle which is inscribed

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What is the area of the innermost circle which is inscribed [#permalink]

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23 Jan 2011, 03:11
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74% (00:42) correct 26% (00:54) wrong based on 167 sessions

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What is the area of the innermost circle which is inscribed in the square?

(1) Area of the ABCD is square 49.
(2) Circumference of the outermost circle is 7Πcm.
[Reveal] Spoiler: OA

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Re: Area of the innermost circle which is inscribed in the s [#permalink]

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23 Jan 2011, 03:39
MichelleSavina wrote:
Q) What is the area of the innermost circle which is inscribed in the square?
(1) Area of the ABCD is square 49.
(2) Circumference of the outermost circle is 7Πcm.

What is the area of the innermost circle which is inscribed in the square?

Knowing the length of a side of a square is sufficient to calculate the radius of the inscribed or circumscribed circle (the length of a side defines the radius of the inscribed or circumscribed circle) and vise-versa: knowing the length of a radius is sufficient to to calculate the side of the inscribed or circumscribed square.

(1) Area of the ABCD is square 49 --> we can get the length of a side and then going step by step get the radius of the innermost circle to calculate the area. Sufficient.

(2) Circumference of the outermost circle is 7Πcm --> we can get the radius of this circle and then going step by step get the radius of the innermost circle to calculate the area. Sufficient.

For more check: math-circles-87957.html and math-triangles-87197.html

Please post PS questions in the PS subforum: gmat-problem-solving-ps-140/ and DS questions in the DS subforum: gmat-data-sufficiency-ds-141/

Topic moved to the DS subforum.
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Re: Area of the innermost circle which is inscribed in the s [#permalink]

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23 Jan 2011, 03:46
MichelleSavina wrote:
What is the area of the innermost circle which is inscribed in the square?
(1) Area of the ABCD is square 49.
(2) Circumference of the outermost circle is 7Πcm.

Just remember the fact that whenever some regular shape is inscribed or circumscribed in another regular shape, always there exists a relation between their area. Here regular shape means circle, equilateral triangle or square or regular pentagon/hexagon etc.

Statement 1: We know the are of the square ABCD. Hence, we can determine the areas of the inner shapes.

Sufficient

Statement 2: We know the radius of the outermost circle. Hence we can determine the lengths of sides or radius of the inner shapes and hence their areas.

Sufficient

[Reveal] Spoiler:

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Re: Area of the innermost circle which is inscribed in the s [#permalink]

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23 Jan 2011, 07:49
Bunuel wrote:

Please post PS questions in the PS subforum: gmat-problem-solving-ps-140/ and DS questions in the DS subforum: gmat-data-sufficiency-ds-141/

Topic moved to the DS subforum.

Sorry about that... i was in a hurry, so did it by mistake.. ...

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Re: Area of the innermost circle which is inscribed in the s [#permalink]

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24 Jan 2011, 09:24
Bunuel wrote:
MichelleSavina wrote:
Q) What is the area of the innermost circle which is inscribed in the square?
(1) Area of the ABCD is square 49.
(2) Circumference of the outermost circle is 7Πcm.

What is the area of the innermost circle which is inscribed in the square?

Knowing the length of a side of a square is sufficient to calculate the radius of the inscribed or circumscribed circle (the length of a side defines the radius of the inscribed or circumscribed circle) and vise-versa: knowing the length of a radius is sufficient to to calculate the side of the inscribed or circumscribed square.

(1) Area of the ABCD is square 49 --> we can get the length of a side and then going step by step get the radius of the innermost circle to calculate the area. Sufficient.

(2) Circumference of the outermost circle is 7Πcm --> we can get the radius of this circle and then going step by step get the radius of the innermost circle to calculate the area. Sufficient.

For more check: math-circles-87957.html and math-triangles-87197.html

Please post PS questions in the PS subforum: gmat-problem-solving-ps-140/ and DS questions in the DS subforum: gmat-data-sufficiency-ds-141/

Topic moved to the DS subforum.

can you please describe more clearly? i dont understand...
it askes us to find what the area of the INNERMOST circle... we surely know the length of sides of ABCD and also know radius of circle but we dont know the area of the inner square so how could we find the radius of the innermost circle???

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Re: Area of the innermost circle which is inscribed in the s [#permalink]

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24 Jan 2011, 09:45
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Expert's post
diebeatsthegmat wrote:
Bunuel wrote:
MichelleSavina wrote:
Q) What is the area of the innermost circle which is inscribed in the square?
(1) Area of the ABCD is square 49.
(2) Circumference of the outermost circle is 7Πcm.

What is the area of the innermost circle which is inscribed in the square?

Knowing the length of a side of a square is sufficient to calculate the radius of the inscribed or circumscribed circle (the length of a side defines the radius of the inscribed or circumscribed circle) and vise-versa: knowing the length of a radius is sufficient to to calculate the side of the inscribed or circumscribed square.

(1) Area of the ABCD is square 49 --> we can get the length of a side and then going step by step get the radius of the innermost circle to calculate the area. Sufficient.

(2) Circumference of the outermost circle is 7Πcm --> we can get the radius of this circle and then going step by step get the radius of the innermost circle to calculate the area. Sufficient.

For more check: math-circles-87957.html and math-triangles-87197.html

Please post PS questions in the PS subforum: gmat-problem-solving-ps-140/ and DS questions in the DS subforum: gmat-data-sufficiency-ds-141/

Topic moved to the DS subforum.

can you please describe more clearly? i dont understand...
it askes us to find what the area of the INNERMOST circle... we surely know the length of sides of ABCD and also know radius of circle but we dont know the area of the inner square so how could we find the radius of the innermost circle???

If you know the length of a side of a square then you can get the radius of inscribed circle: $$2R=S$$ --> $$R=\frac{S}{2}$$;

Next, if you know the radius of a circle you can get the length of a side of inscribed square: $$(2R)^2=s^2+s^2$$ --> $$s=R*\sqrt{2}$$;

So going step by step you can get the radius of the innermost circle to calculate the area of it.

Hope it's clear.
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Re: What is the area of the innermost circle which is inscribed [#permalink]

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12 Jul 2013, 02:59
Bumping for review and further discussion.
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Re: Area of the innermost circle which is inscribed in the s [#permalink]

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05 Oct 2013, 09:09
Bunuel wrote:
MichelleSavina wrote:
Q) What is the area of the innermost circle which is inscribed in the square?
(1) Area of the ABCD is square 49.
(2) Circumference of the outermost circle is 7Πcm.

What is the area of the innermost circle which is inscribed in the square?

Knowing the length of a side of a square is sufficient to calculate the radius of the inscribed or circumscribed circle (the length of a side defines the radius of the inscribed or circumscribed circle) and vise-versa: knowing the length of a radius is sufficient to to calculate the side of the inscribed or circumscribed square.

(1) Area of the ABCD is square 49 --> we can get the length of a side and then going step by step get the radius of the innermost circle to calculate the area. Sufficient.

(2) Circumference of the outermost circle is 7Πcm --> we can get the radius of this circle and then going step by step get the radius of the innermost circle to calculate the area. Sufficient.

Also , as per gmat quant book by bunuel .... We can find out the area of circle inscribed in a square as per the points mentioned below.

• If a circle is circumscribed around a square, the area of the circle is (about 1.57) times the area of the square.
• If a circle is inscribed in the square, the area of the circle is (about 0.79) times the area of the square.

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Re: What is the area of the innermost circle which is inscribed [#permalink]

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16 Nov 2016, 12:42
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: What is the area of the innermost circle which is inscribed   [#permalink] 16 Nov 2016, 12:42
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