Scott Woodbury-Stewart

GMAT OFFICIAL GUIDE DS – The figure above represents an L-shaped garden…

The figure above represents an L-shaped garden…

Solution:

We are given a diagram of an L-shaped garden. Let’s sketch that diagram below.

Screen Shot 2016-05-16 at 7.37.52 PM

We see that the L-shaped garden can be broken up into smaller shapes. Let’s sketch that below.

Statement One Alone: 

The area of the garden is 189 square feet.

Using our diagram of smaller shapes and the information from statement one we can create the following equation:

(15)(k) + (15 – k)(k) + = 189

15k + 15k – k^2 = 189

k^2 – 30k + 189 = 0

(k – 9)(k – 21) = 0

k = 9 or k = 21

Referencing our diagram we see that k cannot be 21; thus, k must be 9.  Statement one alone is sufficient to answer the question.  We can eliminate answer choices B, C, and E.

Statement Two Alone: 

The perimeter of the garden is 60 feet.

Using our diagram of smaller shapes and the information from statement two we can create the following equation:

k + (15 – k) + k + 15 + k + (15 – k) + (15 – k) = 60

60 = 60

Notice that all the occurrences of k canceled out.  Thus, we cannot determine a value for k.  Statement two alone is not sufficient to answer the question.

Answer: A 

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