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QOTD #10 The length of each side of rectangle R is integer

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QOTD #10 The length of each side of rectangle R is integer [#permalink] New post   14 Aug 2016, 06:52
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The length of each side of rectangle R is an integer, and the area of R is 36.

Quantity A
Quantity B
Number of possible values of perimeter of R
6


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.

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Re: QOTD #10 The length of each side of rectangle R is integer [#permalink] New post   14 Aug 2016, 06:52
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Explanation

Because the length of each side of rectangle R is an integer and each length is a factor of the area 36, there are 5 possible rectangles: a 1 × 36 rectangle, a 2 × 18 rectangle, a 3 x 12 rectangle, a 4 × 9 rectangle, and a 6 × 6 rectangle.

The perimeter of the 1 × 36 rectangle is 2(1 + 36), or 74.
The perimeter of the 2 × 18 rectangle is 2(2 + 18), or 40.
The perimeter of the 3 × 12 rectangle is 2(3 + 12), or 30.
The perimeter of the 4 × 9 rectangle is 2(4 + 9), or 26.
The perimeter of the 6 × 6 rectangle is 2(6 + 6), or 24.

Since each of the 5 possible rectangles has a different perimeter, Quantity A, the number of possible values of the perimeter, is 5. Since Quantity B is 6, the correct answer is Choice B.
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Re: QOTD #10 The length of each side of rectangle R is integer [#permalink] New post   25 Jan 2017, 09:11
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roshangre wrote:
Why the length can't more than 7? Say, if length=7, breadth will be 36/7 and so on ? The information is only about length being an integer, it hasn't said anything about breadth, I mean it doesnot say if breadth is an integer as well.


When we are growing up, we learn that the area of a rectangle is length x width, and this sets us up to have incorrect theories concerning what we call the sides of a rectangle.
Many people call the vertical side the length and the horizontal side the width. Others call the longest side the length and the shortest side the width.
None of this is true.

Length does not refer to the arbitrary side of a rectangle. Length refers to the distance from one point to another.

The question says, "The length of each side of rectangle R is an integer, and the area of R is 36"
The word length is not referring to a specific side of the rectangle; it is referring to every side of the rectangle.

I hope that helps.

Cheers,
Brent
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Re: QOTD #10 The length of each side of rectangle R is integer [#permalink] New post   24 Jan 2017, 02:03
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Why the length can't more than 7? Say, if length=7, breadth will be 36/7 and so on ? The information is only about length being an integer, it hasn't said anything about breadth, I mean it doesnot say if breadth is an integer as well.
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Re: QOTD #10 The length of each side of rectangle R is integer [#permalink] New post   24 Jan 2017, 03:01
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roshangre wrote:
Why the length can't more than 7? Say, if length=7, breadth will be 36/7 and so on ? The information is only about length being an integer, it hasn't said anything about breadth, I mean it doesnot say if breadth is an integer as well.


Your argument makes sense. This is the official ETS explanation. It is very unusual that ETS makes mistakes such as this one.
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Re: QOTD #10 The length of each side of rectangle R is integer [#permalink] New post   19 Jun 2017, 09:28
Hi,

One of the options that they give is a 6X6 rectangle...but a rectangle doesn't have four equal sides. It would be a square, right? I know that option B would still be the right answer regardless but if 6x6 is considered a square wouldn't it be four values for the perimeter rather than 5? Hope this makes sense.
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Re: QOTD #10 The length of each side of rectangle R is integer [#permalink] New post   14 Sep 2017, 23:51
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ireland17 wrote:
Hi,

One of the options that they give is a 6X6 rectangle...but a rectangle doesn't have four equal sides. It would be a square, right? I know that option B would still be the right answer regardless but if 6x6 is considered a square wouldn't it be four values for the perimeter rather than 5? Hope this makes sense.


A square is still a rectangle. A special type but a rectangle.
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QOTD #10 The length of each side of rectangle R is integer [#permalink] New post   27 May 2019, 08:51
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A square is still a rectangle. A special type but a rectangle

We can add to this....

A parallelogram is a special kind of quadrilateral
A rectangle is a special kind of parallelogram
A square is a special kind of rectangle


We can also write:
A parallelogram is a special kind of quadrilateral
A rhombus is a special kind of parallelogram
A square is a special kind of rhombus
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Re: QOTD #10 The length of each side of rectangle R is integer [#permalink] New post   01 Jul 2022, 22:08
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