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

Expert's post

00:00

Question Stats:

85% (01:01) correct
14% (00:32) wrong based on 47 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.

Re: The area of a square [#permalink]
26 Jun 2018, 09:55

1

This post received KUDOS

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]
30 Jun 2018, 06:56

1

This post received KUDOS

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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