A circular garden is surrounded by a fence of negligible width along

Hi All,

This question can be solved algebraically or by TESTing THE ANSWERS.

We're told that the circumference of a circular garden = 1/2 the area of the garden. We're asked for the RADIUS of the garden.

Let's TEST Answer B: 2

IF....Radius = 2
Circumference = 2(pi)R = 4pi
Area = (pi)R^2 = 4pi
This circumference is NOT half the area.
Eliminate Answer B. We need the area to be BIGGER...

Next, Let's TEST Answer D: 8

IF....Radius = 8
Circumference = 2(pi)R = 16pi
Area = (pi)R^2 = 64pi
This circumference is NOT half the area (it's 1/4 of the area).
Eliminate Answer D. We need the area to be SMALLER...

There's only one answer left...

Final Answer:

Here's proof that it's correct:

IF....Radius = 4
Circumference = 2(pi)R = 8pi
Area = (pi)R^2 = 16pi
This circumference IS half the area, so this MUST be the answer.

GMAT assassins aren't born, they're made,
Rich

2 pi r= pi r^2/2

r= 4
imo c

Formula based question and test takers should be able to complete such questions in less than 60 sec.
Length of the fence = length of the circular garden = circumference of the circular region = 2πr
According to the condition, length of the fence is 1/2 of the area of the garden (πr^2)
Therefore, 2πr = 1/2 x (πr^2)
Solving the above equation, r = 4

Hence, the answer is option C. 4

Tip: Always write what you're solving for. Sometimes questions ask you to find diameter, or some other value. Do no blindly solve such each questions because there're some deadly traps