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The area of a square

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The area of a square [#permalink] New post 26 Jun 2018, 09:12
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Question Stats:

85% (01:07) correct 14% (00:23) wrong based on 35 sessions
Quantity A
Quantity B
The area of a square region with the perimeter of 24
The area of a rectangular region with the perimeter of 28


A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.
[Reveal] Spoiler: OA

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Re: The area of a square [#permalink] New post 26 Jun 2018, 09:55
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Carcass wrote:
Quantity A
Quantity B
The area of a square region with the perimeter of 24
The area of a rectangular region with the perimeter of 28


A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.


From Statement 1 we have

Perimeter of Square = 4 * side =24

or side = 6

Now area of square = \(6^2\) =36

From Statement 2;

Perimeter of rectangle = 2(Length * Breadth) = 28

or Length * Breadth = 14

Now suppose Length = 4 and breadth = 10

Then area of rectangle = Length * Breadth = 40 ; which is greater than Statement 1

But if Length = 2 and Breadth = 12

Then area of rectangle = Length * Breadth = 24 ; which is Less than Statement 1

Hence the option is D
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Re: The area of a square [#permalink] New post 30 Jun 2018, 06:56
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Expert's post
Carcass wrote:
Quantity A
Quantity B
The area of a square region with the perimeter of 24
The area of a rectangular region with the perimeter of 28


A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.


Notice that Quantity A is FIXED.
All sides of a square have the same length
So, if the perimeter is 24, then each side has length 6
So, the area of the square = (base)(height) = (6)(6) = 36
So, QUANTITY A = 36


On the other hand, Quantity B can have infinitely many values
Consider these two possible cases:

CASE A: if the perimeter of the rectangle is 28, then its dimensions could be 6 by 8
In this case, the area = (base)(height) = (6)(8) = 48
Since QUANTITY A = 36, we can see that Quantity B is greater

CASE B: if the perimeter of the rectangle is 28, then its dimensions could also be 1 by 13
In this case, the area = (base)(height) = (1)(13) = 13
Since QUANTITY A = 36, we can see that Quantity A is greater

Answer: D

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Re: The area of a square   [#permalink] 30 Jun 2018, 06:56
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