The figure above represents an \(L\)shaped garden. What is the value of \(k?\)
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(1) The area of the garden is \(189\) square feet.
(2) The perimeter of the garden is \(60\) feet.
Answer: A
Source: Official Guide
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Target question: What is the value of k?Gmat_mission wrote: ↑Thu Jan 07, 2021 10:50 am20151026_2054.png
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.
Answer: A
Source: Official Guide
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 = 9
Since 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 = 6
Case b:
Notice that the perimeter = 60
In this case, the answer to the target question is k = 5
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT
Answer: A
Cheers,
Brent