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
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