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505-555 (Easy)|   Geometry|      
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Bunuel
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If the number of square units in the area of a circle is A and the nu 15 Feb 2018, 23:37
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15% (low)

Question Stats:

83% (01:36) correct 17% (01:44) wrong based on 98 sessions

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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
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A
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If the number of square units in the area of a circle is A and the nu 16 Feb 2018, 00:02
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Bunuel
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
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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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If the number of square units in the area of a circle is A and the nu 16 Feb 2018, 00:05
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Bunuel
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
Show more


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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If the number of square units in the area of a circle is A and the nu 07 Aug 2019, 21:14
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Bunuel
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
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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 07 Nov 2019, 22:06
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amanvermagmat
Bunuel
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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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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If the number of square units in the area of a circle is A and the nu 08 Nov 2019, 00:51
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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
amanvermagmat
Bunuel
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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