Welcome to the LEAP Q&A Forum

Find your questions answered. Here.

GMAT - Data Sufficiency - Geometry

The length of the edging that surrounds circular garden K is 1/2 the length of the edging that surrounds circular garden G. What is the area of garden K (Assume that the edging has negligible width.)

The length of the edging that surrounds circular garden K is 1/2 the length of the edging that surrounds circular garden G. What is the area of garden K (Assume that the edging has negligible width.)

(1) The area of G is 25π square meters.
(2) The edging around G is 10π meters long.

Given

Circumference of Garden K = 1/2 Circumeference of Garden G

2πrk = 1/2 2π rg

rk = 1/2 rg .. (i)

Statement 1:

The area of G is 25π square meters.

πrg2 = 25π

rg = 5

rk = 5/2 = 2.5

area of k = πrk2 = π2.52 = 6.25π

Sufficient

 

Statement 2:

The edging around G is 10π meters long.

2πrg = 10π

rg = 5

rk = 2.5

Same answer as statement 1

sufficient