GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

 It is currently 02 Jun 2020, 07:33

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

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

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 64169
If the number of square units in the area of a circle is A and the nu  [#permalink]

### Show Tags

15 Feb 2018, 22:37
00:00

Difficulty:

15% (low)

Question Stats:

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

### HideShow timer Statistics

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

_________________
Retired Moderator
Joined: 21 Aug 2013
Posts: 1359
Location: India
Re: If the number of square units in the area of a circle is A and the nu  [#permalink]

### Show Tags

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.

Current Student
Joined: 07 Jan 2016
Posts: 1082
Location: India
GMAT 1: 710 Q49 V36
Re: If the number of square units in the area of a circle is A and the nu  [#permalink]

### Show Tags

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
Intern
Joined: 21 May 2019
Posts: 2
Re: If the number of square units in the area of a circle is A and the nu  [#permalink]

### Show Tags

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?
Intern
Joined: 13 Aug 2019
Posts: 26
Location: India
Concentration: Strategy, Marketing
WE: Analyst (Retail)
If the number of square units in the area of a circle is A and the nu  [#permalink]

### Show Tags

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.

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.
Director
Joined: 08 Aug 2017
Posts: 729
Re: If the number of square units in the area of a circle is A and the nu  [#permalink]

### Show Tags

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.

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