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The figure above represents an Lshaped garden. What is the value of k
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26 Oct 2015, 08:55
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The figure above represents an Lshaped 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. Kudos for a correct solution.Attachment:
20151026_2054.png [ 4.57 KiB  Viewed 34074 times ]
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Re: The figure above represents an Lshaped garden. What is the value of k
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27 Oct 2015, 12:15
Bunuel wrote: The figure above represents an Lshaped 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. Kudos for a correct solution.Attachment: 20151026_2054.png Stmt (1)  The area of the garden, if it were a square, would be 225 sq ft. The area of the Lshaped garden is 189 sq. ft  which is 36 sq ft less than a 15 x 15 square. Additionally, the missing piece is also a square and we can conclude that its dimensions are 6 x 6. The value of k is therefore 15  6, or 9. SUFFICIENT Stmt (2) The perimeter of the garden will be 60 regardless of the value of k. For example, if k =5, the garden would have dimensions of 15, 5, 10, 10, 5 and 15 (total of 60). If k = 6, the garden's dimensions would be 15, 6, 9, 9, 6 and 15 (again total of 60). NOT SUFFICIENT Answer is A.
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Re: The figure above represents an Lshaped garden. What is the value of k
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26 Jun 2016, 11:01
Bunuel wrote: The figure above represents an Lshaped 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. Kudos for a correct solution.Attachment: 20151026_2054.png Statement 1. Area=15k+(15k)k=189 Hence 30k(k^2)=189 ==> (k^2)+30k189=0 D=b^2  4ac= 900  4(1)(189)=144 Hence k=(30 +12)/(2)=9 or k= (3012)(2)=21 But k<15 hence k=9 Sufficient Statement 2. Perimeter = 15+15+2k+(15k) + (15k)=60 ==> 60=60 k is eliminated Hence statement 2 is not sufficient Answer A
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Re: The figure above represents an Lshaped garden. What is the value of k
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11 Dec 2017, 14:03
Hi All, 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 Lshaped garden is essentially a big square with a small squareshaped corner removed (and the length of a side on that square is (15K)). 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: GMAT assassins aren't born, they're made, Rich
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Re: The figure above represents an Lshaped garden. What is the value of k
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13 Feb 2019, 07:28
Bunuel wrote: The figure above represents an Lshaped 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: 20151026_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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Re: The figure above represents an Lshaped garden. What is the value of k
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02 Jul 2018, 04:10
Blackishmamba wrote: I reached the second option through algebraic approach, which returns the exact value of k=7.5 Sum of all sides = 3(15k)+k+30= 60. Which reduces to k=7.5. Could anyone please point out where I'm making mistake???
Posted from my mobile device The perimeter = 15 + 15 + k + k + (15  k) + (15  k) = 60. k's would cancel and you'd get 60 = 60.
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Re: The figure above represents an Lshaped garden. What is the value of k
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08 Aug 2016, 06:43
santro789 wrote: Can someone please explain me this question in detail step by step. How could we assume the missing the piece as square ? Santro, The lengths of the two complete sides are 15 while the lengths of the two smaller sides are both k. If you imagine a square with sides of 15, then you can (hopefully) see that the missing piece has two sides that are 15  k in length. Now, looking at the measure of the angles, we can also see that this missing piece has all 90 degree angles. Thus, it is either a rectangle or square. But, since the top piece is 15 k in length and the left side piece is 15  k in length AND they are both parallel to the sides opposite them, we can conclude that the missing piece is also a square.



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Re: The figure above represents an Lshaped garden. What is the value of k
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26 Jul 2018, 14:59
Hi Omar31Peru, Yes, you can deal with the information in Fact 1 by setting up a Quadratic equation (although it comes with a 'tweak' to the logic). You can start with your equation and simplify as follows: (15)(K) + (K)(15K) = 189 15K + 15K  K^2 = 189 30K  K^2 = 189 0 = K^2  30K + 189 0 = (K9)(K21) K = 9 or 21 Based on what we know about the garden, K CANNOT be 21, so the only possible value would be K=9. Thus, Fact 1 is SUFFICIENT. GMAT assassins aren't born, they're made, Rich
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Re: The figure above represents an Lshaped garden. What is the value of k
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25 May 2020, 03:02
Bunuel wrote: The figure above represents an Lshaped 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. Kudos for a correct solution.Attachment: 20151026_2054.png 1) 225  189 = (15  k)^2 6 = 15  k k = 9 => Sufficient 2) 15 + 15 + 15 k + 15 k + 2k = 60 60 = 60 => Not Sufficient ANSWER: A



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Re: The figure above represents an Lshaped garden. What is the value of k
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30 May 2020, 10:48
livfcind wrote: VeritasPrepDennis wrote: Bunuel wrote: The figure above represents an Lshaped 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. Kudos for a correct solution.Attachment: 20151026_2054.png Stmt (1)  The area of the garden, if it were a square, would be 225 sq ft. The area of the Lshaped garden is 189 sq. ft  which is 36 sq ft less than a 15 x 15 square. Additionally, the missing piece is also a square and we can conclude that its dimensions are 6 x 6. The value of k is therefore 15  6, or 9. SUFFICIENT Stmt (2) The perimeter of the garden will be 60 regardless of the value of k. For example, if k =5, the garden would have dimensions of 15, 5, 10, 10, 5 and 15 (total of 60). If k = 6, the garden's dimensions would be 15, 6, 9, 9, 6 and 15 (again total of 60). NOT SUFFICIENT Answer is A. How can we conclude that the missing piece is a square? I used the following equation=> =(15k)*k=36=> k=3 or 12 Both are viable answers so I couldnt prove this was sufficient. What did i get wrong? Hi livfcind, To start, there's an error in your equation. The two dimensions of the "missing upperleft corner" are BOTH (15  K) and since we are clearly dealing with 90degree angles, that 'corner' would have to be a square. Based on the information in Fact 1, if you want to create an equation that will account for the "missing upperleft corner" of the picture, then the equation would be... (15  K)(15  K) = 36 (15  K)^2 = 36 So, what numbers, when 'squared', equal 36? The answer is +6 or 6 (but since we're dealing with a geometric shape, we can't have a "negative length", so that corner is a 6x6 square and the value of K must be 9. GMAT assassins aren't born, they're made, Rich
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Re: The figure above represents an Lshaped garden. What is the value of k
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06 Aug 2016, 03:42
Can someone please explain me this question in detail step by step. How could we assume the missing the piece as square ?



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Re: The figure above represents an Lshaped garden. What is the value of k
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01 Jul 2018, 20:19
I reached the second option through algebraic approach, which returns the exact value of k=7.5 Sum of all sides = 3(15k)+k+30= 60. Which reduces to k=7.5. Could anyone please point out where I'm making mistake??? Posted from my mobile device
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Re: The figure above represents an Lshaped garden. What is the value of k
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26 Jul 2018, 13:47
Bunuel wrote: Blackishmamba wrote: I reached the second option through algebraic approach, which returns the exact value of k=7.5 Sum of all sides = 3(15k)+k+30= 60. Which reduces to k=7.5. Could anyone please point out where I'm making mistake???
Posted from my mobile device The perimeter = 15 + 15 + k + k + (15  k) + (15  k) = 60. k's would cancel and you'd get 60 = 60. Hi, Can we solve this problem if we consider two rectangle areas: 15 x K (first) + K (15K) (second) =189 ? , I tried with this but can´t get the solution.



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Re: The figure above represents an Lshaped garden. What is the value of k
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30 Sep 2018, 21:30
why the article before "Lshaped garden" is "an" but not "a"?



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Re: The figure above represents an Lshaped garden. What is the value of k
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30 Sep 2018, 22:42
alienetie1217 wrote: why the article before "Lshaped garden" is "an" but not "a"? Hi alienetie1217, The pronunciation of "Lshaped" is "ehl' NOT 'll'. Hence it starts with "AN" NOT "A".
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Re: The figure above represents an Lshaped garden. What is the value of k
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30 May 2020, 08:10
VeritasPrepDennis wrote: Bunuel wrote: The figure above represents an Lshaped 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. Kudos for a correct solution.Attachment: 20151026_2054.png Stmt (1)  The area of the garden, if it were a square, would be 225 sq ft. The area of the Lshaped garden is 189 sq. ft  which is 36 sq ft less than a 15 x 15 square. Additionally, the missing piece is also a square and we can conclude that its dimensions are 6 x 6. The value of k is therefore 15  6, or 9. SUFFICIENT Stmt (2) The perimeter of the garden will be 60 regardless of the value of k. For example, if k =5, the garden would have dimensions of 15, 5, 10, 10, 5 and 15 (total of 60). If k = 6, the garden's dimensions would be 15, 6, 9, 9, 6 and 15 (again total of 60). NOT SUFFICIENT Answer is A. How can we conclude that the missing piece is a square? I used the following equation=> =(15k)*k=36=> k=3 or 12 Both are viable answers so I couldnt prove this was sufficient. What did i get wrong?




Re: The figure above represents an Lshaped garden. What is the value of k
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