Welcome to the LEAP Q&A Forum

Find your questions answered. Here.

GMAT - Data Sufficiency - Geometry

The figure above represents an L-shaped garden. What is the value of k?

 

The figure above represents an L-shaped garden. What is the value of k?

(1) The area of the garden is 189 square feet.
(2) The perimeter of the garden is 60 feet.

Area of the shaded portion = area of larger square - area of smaller square = 152 - (15 - k)2 = 30k - k2 .... (a)

Perimeter of shaded portion = 2*15 + 2*k  + 15 - k + 15 - k = 60

Perimeter is independent of k.. (b)

(1) The area of the garden is 189 square feet.

from equation (a)

189 = 30k - k2 

k2 - 30k + 189 = 0

k2 - 21k - 9k + 189 = 0

k (k - 21) - 9 (k - 21) = 0

k = 21 or k = 9

but k has to be less than 15

thus k = 9

sufficient


(2) The perimeter of the garden is 60 feet.

from equation (b)

perimeter is independent of k. Insufficient.