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.
A
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AbeNeedsAnswers
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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.
A
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Hi AbeNeedsAnswers,
We're asked for the value of K in the drawing. While we normally have to be careful about trusting a picture in a DS question, we can trust the data in the drawing. We know that all of the angles are right angles and we know that the L-shaped garden is essentially a big square with a small square-shaped corner removed (and the length of a side on that square is (15-K)).
1) The area of the garden is 189 square feet.
A 15ft x 15ft square would have an area of 225 sq. ft. Since the garden is 189 sq ft., we know the missing corner = 225 - 189 = 36 sq. ft. This means that each side of that little square would have to be 6. Thus, 15 - K = 6, so K = 9.
Fact 1 is SUFFICIENT
2) The perimeter of the garden is 60 feet.
With this Fact, we can create the following equation (where X is one of the unlabeled sides):
15 + 15 + K + K + X + X = 60
2K + 2X = 30
K + X = 15
This is NOT new information (we knew this from the prompt). Thus, K could be any value in the range of 0 < K < 15.
Fact 2 is INSUFFICIENT
Final Answer: A
GMAT assassins aren't born, they're made,
Rich
We're asked for the value of K in the drawing. While we normally have to be careful about trusting a picture in a DS question, we can trust the data in the drawing. We know that all of the angles are right angles and we know that the L-shaped garden is essentially a big square with a small square-shaped corner removed (and the length of a side on that square is (15-K)).
1) The area of the garden is 189 square feet.
A 15ft x 15ft square would have an area of 225 sq. ft. Since the garden is 189 sq ft., we know the missing corner = 225 - 189 = 36 sq. ft. This means that each side of that little square would have to be 6. Thus, 15 - K = 6, so K = 9.
Fact 1 is SUFFICIENT
2) The perimeter of the garden is 60 feet.
With this Fact, we can create the following equation (where X is one of the unlabeled sides):
15 + 15 + K + K + X + X = 60
2K + 2X = 30
K + X = 15
This is NOT new information (we knew this from the prompt). Thus, K could be any value in the range of 0 < K < 15.
Fact 2 is INSUFFICIENT
Final Answer: A
GMAT assassins aren't born, they're made,
Rich
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Target question: What is the value of k?AbeNeedsAnswers 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.
A
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
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Solution:AbeNeedsAnswers wrote: ↑Tue Aug 22, 2017 7:47 pm
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.
A
Question Stem Analysis:
We need to determine the value of k. Notice that each of the two unlabeled sides has a length of 15 - k ft.
Statement One Alone:
Knowing that the area of the garden is 189 square feet, we can create the equation:
15^2 - (15 - k)^2 = 189
225 - 189 = (15 - k)^2
36 = (15 - k)^2
15 - k = 6 or 15 - k = -6
k = 9 or k = 21
Since k can’t be greater than 15 (otherwise 15 - k would be negative), k = 9. Statement one alone is sufficient.
Statement Two Alone:
Knowing that the perimeter of the garden is 60 feet, we can create the equation:
15 + 15 + k + (15 - k) + (15 - k) + k = 60
Simplifying this equation, we have:
60 = 60
That is, the equation always holds as long as k is any positive value less than 15. Statement two alone is not sufficient.
Answer: A
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Beauty of this question is not in the reasoning or calculation part, but the three traps it sets up for the people solving. Seldom have I seen so many traps in the same question.
Text solution below, however for those interested in detailed step by step solution (video) along with clear call out of the TRAPS/MISTAKES here is a video solution: Solution for Beginners - 50% Get This Wrong Q464 DS02888 L-Shaped Garden
SOLUTION
I am going to start with statement 2
Statement 2: Perimeter = 60
The perimeter of a polygon is sum of all sides of the polygon. In our case, starting from the bottom and going clockwise:
15 + k + (15-k) + (15-k) + k + 15 = 60
This is TRAP 1: With the constraint of time, some would look at this and say "One equation one variable" and mark this as "Sufficient". But thats the trap if you do not simplify this equation. When you simplify you realize that k cancels off and you only get
60 = 60 !! No value of k possible form the given information.
INSUFF
Statement 1: Area = 189
Pretty easy to come to the quadratic
k^2 - 30k + 189 = 0
TRAP 2: If you stop here and say - obviously k is not unique since 2 possible values of k possible. Hence insufficient. You will be falling into the trap 2. Remember - one of the values of k could be negative or discarded, so you must keep on going here.
k=9 or k=21
TRAP 3: If you stop here and say - well I expected 2 values and I got two "+ve" values of k. No unique answer hence INSUFF! You will be falling into the trap 3 after all the hard work! Just take a step further and check the "feasibility of the two values"
k=9 : possible
k=21: impossible because the max side in the polygon is clearly 15. k cannot be more than that . So we must discard
So only k=9 possible. Hence (A) is sufficient to answer the question
(A)
Check out the video for clear takeaways! Also An EXPERT TIP, chalk this up as one of the most important questions you have to review few days before the exam so you don't fall for these traps.
Text solution below, however for those interested in detailed step by step solution (video) along with clear call out of the TRAPS/MISTAKES here is a video solution: Solution for Beginners - 50% Get This Wrong Q464 DS02888 L-Shaped Garden
SOLUTION
I am going to start with statement 2
Statement 2: Perimeter = 60
The perimeter of a polygon is sum of all sides of the polygon. In our case, starting from the bottom and going clockwise:
15 + k + (15-k) + (15-k) + k + 15 = 60
This is TRAP 1: With the constraint of time, some would look at this and say "One equation one variable" and mark this as "Sufficient". But thats the trap if you do not simplify this equation. When you simplify you realize that k cancels off and you only get
60 = 60 !! No value of k possible form the given information.
INSUFF
Statement 1: Area = 189
Pretty easy to come to the quadratic
k^2 - 30k + 189 = 0
TRAP 2: If you stop here and say - obviously k is not unique since 2 possible values of k possible. Hence insufficient. You will be falling into the trap 2. Remember - one of the values of k could be negative or discarded, so you must keep on going here.
k=9 or k=21
TRAP 3: If you stop here and say - well I expected 2 values and I got two "+ve" values of k. No unique answer hence INSUFF! You will be falling into the trap 3 after all the hard work! Just take a step further and check the "feasibility of the two values"
k=9 : possible
k=21: impossible because the max side in the polygon is clearly 15. k cannot be more than that . So we must discard
So only k=9 possible. Hence (A) is sufficient to answer the question
(A)
Check out the video for clear takeaways! Also An EXPERT TIP, chalk this up as one of the most important questions you have to review few days before the exam so you don't fall for these traps.
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