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If the number of square units in the area of a circle is A and the nu

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If the number of square units in the area of a circle is A and the nu  [#permalink]

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New post 15 Feb 2018, 22:37
00:00
A
B
C
D
E

Difficulty:

  15% (low)

Question Stats:

83% (01:35) correct 17% (01:48) wrong based on 87 sessions

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Re: If the number of square units in the area of a circle is A and the nu  [#permalink]

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New post 15 Feb 2018, 23:02
Bunuel wrote:
If the number of square units in the area of a circle is A and the number of linear units in the circumference is C, what is the radius of the circle?

(1) A/C = 3/2

(2) A > C + 3


Let 'r' be the radius of a circle. Then its area, A = π*r^2 and its Circumference C = 2*π*r.

Statement 1

Ratio of A:C = A/C = (π*r^2)/(2*π*r) = r/2
This is given to us as 3/2. Equating r/2 = 3/2 or r=3. Sufficient.

Statement 2

A > C + 3
π*r^2 > 2*π*r + 3 or π*r(r-2) > 3
This will not help us in calculating r. Not sufficient.

Hence A answer
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Re: If the number of square units in the area of a circle is A and the nu  [#permalink]

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New post 15 Feb 2018, 23:05
Bunuel wrote:
If the number of square units in the area of a circle is A and the number of linear units in the circumference is C, what is the radius of the circle?

(1) A/C = 3/2

(2) A > C + 3



Area of a circle = pi r^2
Circumference = 2pi r

Statement 1: Given A/C = 3/2

pi r^2/ 2pi r = 3/2

r/2=3/2
r= 3

Statement 2 A>C + 3

pi r^2 - 2 pi r > 3

pi ( r^2 - 2r) > 3

r can take multiple values as pi itself is greater than 3

insufficient

(A) imo
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Re: If the number of square units in the area of a circle is A and the nu  [#permalink]

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New post 07 Aug 2019, 20:14
Bunuel wrote:
If the number of square units in the area of a circle is A and the number of linear units in the circumference is C, what is the radius of the circle?

(1) A/C = 3/2

(2) A > C + 3



Given,

A > C + 3

If we start substituting values for r, we get that after r=3, the equation holds good. Thus we arrive at an unique value of r =3. Hence Option D should be the answer right?
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If the number of square units in the area of a circle is A and the nu  [#permalink]

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New post 07 Nov 2019, 21:06
1
amanvermagmat wrote:
Bunuel wrote:
If the number of square units in the area of a circle is A and the number of linear units in the circumference is C, what is the radius of the circle?

(1) A/C = 3/2

(2) A > C + 3


Let 'r' be the radius of a circle. Then its area, A = π*r^2 and its Circumference C = 2*π*r.

Statement 1

Ratio of A:C = A/C = (π*r^2)/(2*π*r) = r/2
This is given to us as 3/2. Equating r/2 = 3/2 or r=3. Sufficient.

Statement 2

A > C + 3
π*r^2 > 2*π*r + 3 or π*r(r-2) > 3
This will not help us in calculating r. Not sufficient.

Hence A answer


Can you please explain how we took \(A = π*r^2\) (area of the circle) and \(C = 2πr\) (circumference of the circle)
I think A & C actually are as below,

\(Number-of-square-units-in-the-circle, A = \frac{Area-of-the-circle}{area-of-each-square-unit}\) = \(\frac{πr^2}{a^2}\)

Similarly, for \(number-of-units-on-the-circumference-of-the-circle, C = \frac{total-circumference-of-the-circle}{length-of-each-unit-on-the-circumference}\) = \(\frac{2πr}{c}\)

Where, a = side of each square and c = length of each unit on the circumference

What I did was,
Statement 1: \(\frac{A}{C} = \frac{3}{2}\)
\((\frac{π*r^2}{a^2})/(\frac{2πr}{c})\) = 3/2
\(\frac{c*r}{2a^2}\) = \(\frac{3}{2}\)
\(r = \frac{3a^2}{c}\)

So, r(radius of the circle) depends on the area of each square unit and length of each circumference unit, which we do not know, hence Insufficient

Statement2:
\(A > C + 3\)
\(\frac{πr^2}{a^2}\) > \(\frac{2πr}{c}\) + 3

Here also, r(radius of the circle) depends on the area of each square unit and length of each circumference unit, which we do not know, hence Insufficient

Even both statements together are not helpful for the same reason, hence Insufficient option E

Please explain where my understanding is incorrect.
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Re: If the number of square units in the area of a circle is A and the nu  [#permalink]

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New post 07 Nov 2019, 23:51
I appreciate mate who wrote this problem, but he missed in terms of language. Such convoluted and ambiguous language is banned in GMAT.

Your understanding is completely valid. And if someone who has solved this problem might have attempted earlier over another forum.

Harsht7 wrote:
amanvermagmat wrote:
Bunuel wrote:
If the number of square units in the area of a circle is A and the number of linear units in the circumference is C, what is the radius of the circle?

(1) A/C = 3/2

(2) A > C + 3


Let 'r' be the radius of a circle. Then its area, A = π*r^2 and its Circumference C = 2*π*r.

Statement 1

Ratio of A:C = A/C = (π*r^2)/(2*π*r) = r/2
This is given to us as 3/2. Equating r/2 = 3/2 or r=3. Sufficient.

Statement 2

A > C + 3
π*r^2 > 2*π*r + 3 or π*r(r-2) > 3
This will not help us in calculating r. Not sufficient.

Hence A answer


Can you please explain how we took \(A = π*r^2\) (area of the circle) and \(C = 2πr\) (circumference of the circle)
I think A & C actually are as below,

\(Number-of-square-units-in-the-circle, A = \frac{Area-of-the-circle}{area-of-each-square-unit}\) = \(\frac{πr^2}{a^2}\)

Similarly, for \(number-of-units-on-the-circumference-of-the-circle, C = \frac{total-circumference-of-the-circle}{length-of-each-unit-on-the-circumference}\) = \(\frac{2πr}{c}\)

Where, a = side of each square and c = length of each unit on the circumference

What I did was,
Statement 1: \(\frac{A}{C} = \frac{3}{2}\)
\((\frac{π*r^2}{a^2})/(\frac{2πr}{c})\) = 3/2
\(\frac{c*r}{2a^2}\) = \(\frac{3}{2}\)
\(r = \frac{3a^2}{c}\)

So, r(radius of the circle) depends on the area of each square unit and length of each circumference unit, which we do not know, hence Insufficient

Statement2:
\(A > C + 3\)
\(\frac{πr^2}{a^2}\) > \(\frac{2πr}{c}\) + 3

Here also, r(radius of the circle) depends on the area of each square unit and length of each circumference unit, which we do not know, hence Insufficient

Even both statements together are not helpful for the same reason, hence Insufficient option E

Please explain where my understanding is incorrect.
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Re: If the number of square units in the area of a circle is A and the nu   [#permalink] 07 Nov 2019, 23:51

If the number of square units in the area of a circle is A and the nu

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