Bunuel wrote:

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.

Attachment:

2015-10-26_2054.png

Target question: What is the value of k? Statement 1: The area of the garden is 189 square feet. Let's drawn an auxiliary line that divides the shape into two rectangular regions A and B.

Regions A and B have the following measurements.

So, the area of region A = k(15 - k) = 15k - k²

The area of region B = 15k

So, the TOTAL area = 15k - k² + 15k = 30k - k²

Since we're told the area is 189, we can write: 30k - k² = 189

Rearrange to get: k² - 30k + 189 = 0

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

So, EITHER k = 21 OR k = 9

HOLD ON!

k cannot be greater than 15 (since one entire side has length 15)

So, it MUST be the case that

k = 9Since we can answer the

target question with certainty, statement 1 is SUFFICIENT

Statement 2: The perimeter of the garden is 60 feet.This statement provides NO NEW information, because the perimeter will ALWAYS be 60, regardless of the value of k.

Here's why:

If k = the two given sides, then the remaining two sides must both have a length of

15 - k So, when we add all lengths, we get: PERIMETER =

k +

(15 - k) +

(15 - k) +

k + 15 + 15 = 60

If you're not convinced, consider these two possible cases:

Case a:

Notice that the perimeter = 60

In this case, the answer to the target question is

k = 6Case b:

Notice that the perimeter = 60

In this case, the answer to the target question is

k = 5Since we cannot answer the

target question with certainty, statement 2 is NOT SUFFICIENT

Answer: A

Cheers,

Brent

_________________

Test confidently with gmatprepnow.com