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Does the area of square S equal the area of circle C?

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Does the area of square S equal the area of circle C?  [#permalink]

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New post 22 Aug 2018, 22:35
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Does the area of square S equal the area of circle C?

(1) The diameter of circle C equals the length of a side of square S.

(2) The ratio of the area of circle C to the area of square S is less than 1:1.

(A)Statement (1) BY ITSELF is sufficient to answer the question, but statement (2) by itself is not.
(B)Statement (2) BY ITSELF is sufficient to answer the question, but statement (1) by itself is not.
(C)Statements (1) and (2) TAKEN TOGETHER are sufficient to answer the question, even though NEITHER statement BY ITSELF is sufficient.
(D)EITHER statement BY ITSELF is sufficient to answer the question.
(E)Statements (1) and (2) TAKEN TOGETHER are NOT sufficient to answer the question, requiring more data pertaining to the problem.
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Does the area of square S equal the area of circle C?  [#permalink]

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New post 22 Aug 2018, 22:51
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s55day wrote:
Does the area of square S equal the area of circle C?

(1) The diameter of circle C equals the length of a side of square S.

(2) The ratio of the area of circle C to the area of square S is less than 1:1.


Question stem:- Does the area of square S equal the area of circle C?

St1:- The diameter of circle C equals the length of a side of square S.
Or, 2r=a
So, Area of circle=\(\pi*r^2\)=\(3.14r^2\)(Approx.)
Area of square=\(a^2=(2r)^2\)=\(4r^2\)

Between \(3.14r^2\) and \(4r^2\), \(4r^2\) is greater.
Therefore, area of square S is greater than circle C.
Sufficient.

St2:- The ratio of the area of circle C to the area of square S is less than 1:1
Or, \(\frac{\pi*r^2}{a^2} < 1\)
Or, \(\pi*r^2 < a^2\)
Or, area of square S is greater than circle C.
Sufficient.

Ans. (D)
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Re: Does the area of square S equal the area of circle C?  [#permalink]

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New post 22 Aug 2018, 22:59
s55day wrote:
Does the area of square S equal the area of circle C?

(1) The diameter of circle C equals the length of a side of square S.

(2) The ratio of the area of circle C to the area of square S is less than 1:1.

(A)Statement (1) BY ITSELF is sufficient to answer the question, but statement (2) by itself is not.
(B)Statement (2) BY ITSELF is sufficient to answer the question, but statement (1) by itself is not.
(C)Statements (1) and (2) TAKEN TOGETHER are sufficient to answer the question, even though NEITHER statement BY ITSELF is sufficient.
(D)EITHER statement BY ITSELF is sufficient to answer the question.
(E)Statements (1) and (2) TAKEN TOGETHER are NOT sufficient to answer the question, requiring more data pertaining to the problem.


To check : Area of square = area of circle
Statement 1: diameter of circle say d = side of square
Area of circle = \(pi*(d/2)^2\)
Area of square = d^2
We can easily compare if area is equal or not.. We don't need to know the answer though
Sufficient

Statement 2: Area of Circle : Area of Square <1:1
Area of Circle < Area of Square and hence Area of circle =/= Area of square
Sufficient

Answer D
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Does the area of square S equal the area of circle C?  [#permalink]

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New post 23 Aug 2018, 00:31
s55day wrote:
Does the area of square S equal the area of circle C?

(1) The diameter of circle C equals the length of a side of square S.

(2) The ratio of the area of circle C to the area of square S is less than 1:1.

(A)Statement (1) BY ITSELF is sufficient to answer the question, but statement (2) by itself is not.
(B)Statement (2) BY ITSELF is sufficient to answer the question, but statement (1) by itself is not.
(C)Statements (1) and (2) TAKEN TOGETHER are sufficient to answer the question, even though NEITHER statement BY ITSELF is sufficient.
(D)EITHER statement BY ITSELF is sufficient to answer the question.
(E)Statements (1) and (2) TAKEN TOGETHER are NOT sufficient to answer the question, requiring more data pertaining to the problem.


Remember all values related to circle such as area, circumference, diameter etc are dependent on only radius
and all values related to square such as area, perimeter, diagonal are dependent on only the side.
so if we know side and radius you can compare anything


so REQUIREMENT - knowing the values of radius and sides is enough. dont have to calculate any area .

(1) The diameter of circle C equals the length of a side of square S.
side = 2r, so we have both radius related and thus relative area too can be found.. sufficient
but lets see
area of square = \(side^2 = 4r^2\)
area of circle = \(\pi*r^2\)...
4>pi
sufficient

(2) The ratio of the area of circle C to the area of square S is less than 1:1.
gives the info directly..
sufficient

D
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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html


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