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SVP  Joined: 21 Jan 2007
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Location: New York City
What is the difference between the lengths of diagonals of  [#permalink]

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What is the difference between the lengths of diagonals of parallelogram ABCD (BD > AC)

(1) AB - BC = 2
(2) Angle ABC = 30 degrees
Director  Joined: 22 Mar 2011
Posts: 588
WE: Science (Education)
Re: What is the difference between the lengths of diagonals of  [#permalink]

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teal wrote:
What is the difference between the lengths of diagonals of parallelogram $$ABCD$$ ( $$BD \gt AC$$ )?

$$AB - BC = 2$$
$$\angle ABC = 30$$ degrees

OA:E

Here is my reasoning -

A) Difference between two diagonals does not restrict the shape of the quad. If it's shape is closer to rectangle then diff between diagonals is very less as opposed to if you change the quad's shape to move away from being a rectangle. ( Rectangle has equal diags.) - Insuff.

B) One angle =30. Due to the property of Parallelogram, this restricts the other angles to 30, 150, 30 (opp angles equal and adjacent angles supplementary). So we have a definite shape for parallelogram but NOT a fixed size so we can still vary the size. As size will vary, the difference between diagonals should also vary -

Here is my question for Forum moderators - as the size of parallelogram will increase will the difference between it's diagonals also increase , right?? vice versa for decrease???? Please confirm.

For C -

You can still vary the size of the quad, so the difference in diagonals should vary, hence E.

For B:
Given one angle of the parallelogram, all its angles are determined as you mentioned.
So, the "shape" of the parallelogram is uniquely determined, meaning all of them are similar, they are just "smaller" or "larger".
Similarity also means the lengths of the sides and the diagonals (which can also be seen as sides in some triangles, like half of the parallelogram) increase or decrease proportionally, so their difference cannot remain a constant.

For C:
Please, refer to the attached drawing, where y in fact is $$2x+2-x\sqrt{3}$$.
The diagonals then can be expressed in terms of x, but we don't have any specific value for x.

Attachments Parallelogram30.jpg [ 11.92 KiB | Viewed 6012 times ]

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Intern  Joined: 28 Aug 2007
Posts: 37
Re: What is the difference between the lengths of diagonals of  [#permalink]

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bmwhype2 wrote:
What is the difference between the lengths of diagonals of parallelogram ABCD (BD > AC)

1. AB - BC = 2
2. Angle ABC = 30 degrees

E you can keep all points ABC in place and move point B around to achieve any difference in length
Manager  Joined: 08 Nov 2007
Posts: 77
Re: What is the difference between the lengths of diagonals of  [#permalink]

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antihero wrote:
bmwhype2 wrote:
What is the difference between the lengths of diagonals of parallelogram ABCD (BD > AC)

1. AB - BC = 2
2. Angle ABC = 30 degrees

E you can keep all points ABC in place and move point B around to achieve any difference in length

I dont follow - how do you move one point about but not another? If it's a parallelogram, then surely moving one point will move one of the other's if it is to maintain two parallel sides?
Manager  Joined: 08 Nov 2007
Posts: 77
Re: What is the difference between the lengths of diagonals of  [#permalink]

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antihero wrote:
alrussell wrote:
antihero wrote:
bmwhype2 wrote:
What is the difference between the lengths of diagonals of parallelogram ABCD (BD > AC)

1. AB - BC = 2
2. Angle ABC = 30 degrees

E you can keep all points ABC in place and move point B around to achieve any difference in length

I dont follow - how do you move one point about but not another? If it's a parallelogram, then surely moving one point will move one of the other's if it is to maintain two parallel sides?

Still E

Agreed - but how do you move a single point around? Im confused.
Intern  Joined: 20 Sep 2006
Posts: 42
Re: What is the difference between the lengths of diagonals of  [#permalink]

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bmwhype2 wrote:
What is the difference between the lengths of diagonals of parallelogram ABCD (BD > AC)

1. AB - BC = 2
2. Angle ABC = 30 degrees

I am confused to. How can diagonals of a parallelogram be different in length.
They have to be equal in length to satisfy the definition of a parallelogram which is
" A quadrilateral with both pairs of opposite sides parallel and equal in length."
Manager  Joined: 13 May 2010
Posts: 103
Re: What is the difference between the lengths of diagonals of  [#permalink]

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What is the difference between the lengths of diagonals of parallelogram $$ABCD$$ ( $$BD \gt AC$$ )?

$$AB - BC = 2$$
$$\angle ABC = 30$$ degrees

OA:E

Here is my reasoning -

A) Difference between two diagonals does not restrict the shape of the quad. If it's shape is closer to rectangle then diff between diagonals is very less as opposed to if you change the quad's shape to move away from being a rectangle. ( Rectangle has equal diags.) - Insuff.

B) One angle =30. Due to the property of Parallelogram, this restricts the other angles to 30, 150, 30 (opp angles equal and adjacent angles supplementary). So we have a definite shape for parallelogram but NOT a fixed size so we can still vary the size. As size will vary, the difference between diagonals should also vary -

Here is my question for Forum moderators - as the size of parallelogram will increase will the difference between it's diagonals also increase , right?? vice versa for decrease???? Please confirm.

For C -

You can still vary the size of the quad, so the difference in diagonals should vary, hence E.
Director  Joined: 22 Mar 2011
Posts: 588
WE: Science (Education)
Re: What is the difference between the lengths of diagonals of  [#permalink]

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saviop wrote:
bmwhype2 wrote:
What is the difference between the lengths of diagonals of parallelogram ABCD (BD > AC)

1. AB - BC = 2
2. Angle ABC = 30 degrees

I am confused to. How can diagonals of a parallelogram be different in length.
They have to be equal in length to satisfy the definition of a parallelogram which is
" A quadrilateral with both pairs of opposite sides parallel and equal in length."

It says "sides" and not diagonals!!!
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Love GMAT Quant questions and running.
Manager  B
Joined: 10 Mar 2014
Posts: 180
Re: What is the difference between the lengths of diagonals of  [#permalink]

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1
teal wrote:
What is the difference between the lengths of diagonals of parallelogram $$ABCD$$ ( $$BD \gt AC$$ )?

$$AB - BC = 2$$
$$\angle ABC = 30$$ degrees

OA:E

Here is my reasoning -

A) Difference between two diagonals does not restrict the shape of the quad. If it's shape is closer to rectangle then diff between diagonals is very less as opposed to if you change the quad's shape to move away from being a rectangle. ( Rectangle has equal diags.) - Insuff.

B) One angle =30. Due to the property of Parallelogram, this restricts the other angles to 30, 150, 30 (opp angles equal and adjacent angles supplementary). So we have a definite shape for parallelogram but NOT a fixed size so we can still vary the size. As size will vary, the difference between diagonals should also vary -

Here is my question for Forum moderators - as the size of parallelogram will increase will the difference between it's diagonals also increase , right?? vice versa for decrease???? Please confirm.

For C -

You can still vary the size of the quad, so the difference in diagonals should vary, hence E.

HI,

I have couple of queries here.

1. the question is talking about parallelogram. so it can be rectangle ( can not be square or rohumbus) or parallelogram ( oppsite sites and opposite angles are equal)

so what you mean by

"Difference between two diagonals does not restrict the shape of the quad. If it's shape is closer to rectangle then diff between diagonals is very less as opposed to if you change the quad's shape to move away from being a rectangle"

Thanks.
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GMAT 1: 620 Q48 V27 GPA: 1.9
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Re: What is the difference between the lengths of diagonals of  [#permalink]

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bmwhype2 wrote:
What is the difference between the lengths of diagonals of parallelogram ABCD (BD > AC)

(1) AB - BC = 2
(2) Angle ABC = 30 degrees

we can't fix the shape ( parallelogram or rhomus). hence E
Non-Human User Joined: 09 Sep 2013
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Re: What is the difference between the lengths of diagonals of  [#permalink]

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_________________ Re: What is the difference between the lengths of diagonals of   [#permalink] 16 Oct 2019, 22:05
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