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metallicafan
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09 Mar 2012, 09:26
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The area of a rectangular lot is 900 feet. What is the length of the lot?
(1) The length of the lot is 25 feet greater than the width.
(2) If the lot were separated into three unequal sections with two of the sections being square, the remaining section would have a length of 5 feet.
Source: https://www.gmathacks.com
(1) The length of the lot is 25 feet greater than the width.
(2) If the lot were separated into three unequal sections with two of the sections being square, the remaining section would have a length of 5 feet.
Source: https://www.gmathacks.com
09 Mar 2012, 10:56
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Hi, there. I'm happy to help with this. 
Prompt: The area of a rectangular lot is 900 feet. What is the length of the lot?
So, if it has length L and width W, then L*W = 900. So far, we have one equation with two unknowns.
Statement #1: The length of the lot is 25 feet greater than the width.
In other words, L = 25 + W. Now we have two equations with two unknowns. That's a situation in which we are able to solve for definitive values of the variables. As it happens, L = 45, W = 20. Statement #1, by itself, is sufficient.
Statement #2: If the lot were separated into three unequal sections with two of the sections being square, the remaining section would have a length of 5 feet.
What's not clear about this statement is: are all three of the sections unequal, which means the squares have to be different sizes, or it is just saying that not all three of sections are the same dimensions?
If the squares can be the same size, then one solution is possibility #1:
section possibility #1.JPG [ 28.05 KiB | Viewed 3584 times ]
If the squares are not equal, we get a set up like this:
section possibility #2.JPG [ 22.71 KiB | Viewed 3603 times ]
Equating the left and right sides of this figure, we get L - W + 5 = W. That's a second equation relating L and W. As it happens, this gives solutions of L = 40, W = 22.5. Thus, statement #2 produces more than one possibility, so it is insufficient.
Does all this make sense? Please let me know if you have any further question on this.
Mike
Prompt: The area of a rectangular lot is 900 feet. What is the length of the lot?
So, if it has length L and width W, then L*W = 900. So far, we have one equation with two unknowns.
Statement #1: The length of the lot is 25 feet greater than the width.
In other words, L = 25 + W. Now we have two equations with two unknowns. That's a situation in which we are able to solve for definitive values of the variables. As it happens, L = 45, W = 20. Statement #1, by itself, is sufficient.
Statement #2: If the lot were separated into three unequal sections with two of the sections being square, the remaining section would have a length of 5 feet.
What's not clear about this statement is: are all three of the sections unequal, which means the squares have to be different sizes, or it is just saying that not all three of sections are the same dimensions?
If the squares can be the same size, then one solution is possibility #1:
Attachment:
section possibility #1.JPG [ 28.05 KiB | Viewed 3584 times ]
If the squares are not equal, we get a set up like this:
Attachment:
section possibility #2.JPG [ 22.71 KiB | Viewed 3603 times ]
Equating the left and right sides of this figure, we get L - W + 5 = W. That's a second equation relating L and W. As it happens, this gives solutions of L = 40, W = 22.5. Thus, statement #2 produces more than one possibility, so it is insufficient.
Answer = A
Does all this make sense? Please let me know if you have any further question on this.
Mike
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12 Jul 2017, 14:51
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metallicafan
The area of a rectangular lot is 900 feet. What is the length of the lot?
(1) The length of the lot is 25 feet greater than the width.
(2) If the lot were separated into three unequal sections with two of the sections being square, the remaining section would have a length of 5 feet.
Source: https://www.gmathacks.com
(1) The length of the lot is 25 feet greater than the width.
(2) If the lot were separated into three unequal sections with two of the sections being square, the remaining section would have a length of 5 feet.
Source: https://www.gmathacks.com
If I'm thinking about this right...
(1)
Width=X
Length=X+25
X(X+25)=900
1 variable equation needs only 1 question to solve (Kaplan)
Sufficient
(2)
900 - two separate perfect square factors = some number divisible by 5 since length of 3rd rectangle is 5.
Many squares possible to use
Insufficient
A.
