Is quadrilateral Q a square? : Data Sufficiency (DS)

yogachgolf

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Is quadrilateral Q a square? [#permalink]

28 Nov 2007, 15:19

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A

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C

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Is quadrilateral Q a square?

(1) The sides of Q have the same length.
(2) The diagonals of Q have the same length

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Bunuel

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Re: Re: [#permalink]

25 Oct 2013, 08:28

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jlgdr wrote:

shubhampandey wrote:

yogachgolf wrote:

Is quadrilateral Q a square?

(1) The sides of Q have the same length.
(2) The diagonals of Q have the same length

In a parallelogram, not all the sides have the same length from what I understand.
Or am I missing something?

Parallelogram CAN have all 4 sides of equal length.

Parallelogram A quadrilateral with two pairs of parallel sides.

Properties and Tips
• Opposite sides of a parallelogram are equal in length.
• Opposite angles of a parallelogram are equal in measure.
• Opposite sides of a parallelogram will never intersect.
• The diagonals of a parallelogram bisect each other.
• Consecutive angles are supplementary, add to 180°.
• The area, $A$, of a parallelogram is $A = bh$, where $b$ is the base of the parallelogram and $h$ is its height.
• The area of a parallelogram is twice the area of a triangle created by one of its diagonals.

A parallelogram is a quadrilateral with opposite sides parallel and congruent. It is the "parent" of some other quadrilaterals, which are obtained by adding restrictions of various kinds:
• A rectangle is a parallelogram but with all angles fixed at 90°
• A rhombus is a parallelogram but with all sides equal in length
• A square is a parallelogram but with all sides equal in length and all angles fixed at 90°

For other properties check polygons chapter of Math Book: math-polygons-87336.html
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Bunuel

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Re: Re: [#permalink]

15 Apr 2014, 01:19

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pawankumargadiya wrote:

HI Bunnel,

As you have mentioned that Parallelogram can have four sides equal then definitely its diagonals are also equal and it will become square. why A is not right?

If a parallelogram has equal sides it is a rhombus but rhombus is not necessary to have equal diagonals, or in other words not all rhombuses are squares:

Hope it's clear.
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walker

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[#permalink]

28 Nov 2007, 15:40

Expert Reply

С. only both can let us a square.

B

walker

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[#permalink]

28 Nov 2007, 16:05

Expert Reply

yogachgolf wrote:

why 'a' is insuff?

you can imagine four sticks with same length that are pinned by hinges. you can easily transform the square to a different rhombuses and even to a line.

GMATBLACKBELT

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Re: Square [#permalink]

28 Nov 2007, 16:24

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yogachgolf wrote:

Is quadrilateral Q a square?
(1) The sides of Q have the same length.
(2) The diagonals of Q have the same length

C

Here il post u a drawing.

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jakolik

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Re: Geometry DS [#permalink]

05 Aug 2010, 06:24

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Statement 1 is not sufficient since a rhombus has 4 equal sides as well.

Statement 2 is not sufficient since a rectangle has equal diagonals.

Statements 1 and 2 are sufficient.

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Re: [#permalink]

25 Oct 2013, 06:35

shubhampandey wrote:

yogachgolf wrote:

walker wrote:

С. only both can let us a square.

why 'a' is insuff?

Because it can be a parellogram or rhombus..

In a parallelogram, not all the sides have the same length from what I understand.
Or am I missing something?

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PathFinder007

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Re: Re: [#permalink]

15 Apr 2014, 01:10

HI Bunnel,

As you have mentioned that Parallelogram can have four sides equal then definitely its diagonals are also equal and it will become square. why A is not right?

B

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Re: Is quadrilateral Q a square? [#permalink]

05 Jun 2014, 03:43

A is insufficient cause rhombus is a quadrilateral with four sides & diagonals of dfferent lengths
B is insufficient cause a uniform Trapezoid has both the diagonals equal..

C is sufficient as trapezoid and rhombus are both eliminated.Hence a square

B

JusTLucK04

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Re: Square [#permalink]

Updated on: 05 Jun 2014, 05:20

GMATBLACKBELT wrote:

yogachgolf wrote:

Is quadrilateral Q a square?
(1) The sides of Q have the same length.
(2) The diagonals of Q have the same length

C

Here il post u a drawing.

This is an incorrect explanation cause a hexagon is not a quadrilateral and instead a uniform trapezium or a rectangle is a better alternative

Originally posted by JusTLucK04 on 05 Jun 2014, 03:45.
Last edited by JusTLucK04 on 05 Jun 2014, 05:20, edited 1 time in total.

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PerfectScores

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Re: Is quadrilateral Q a square? [#permalink]

05 Jun 2014, 03:50

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yogachgolf wrote:

Is quadrilateral Q a square?

(1) The sides of Q have the same length.
(2) The diagonals of Q have the same length

Statement I is insufficient:

Rhombus have same lengths and so does a square.

Statement II is insufficient:

Sides may or may not be same.

Combining is sufficient:

If sides are same and diagonals are same which means all the sides must intersect at ninety degrees hence answer is c.

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Re: Is quadrilateral Q a square? (1) The sides of Q have the [#permalink]

28 Sep 2015, 01:57

C is the answer as it can be solved by using both the statements.

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Re: Is quadrilateral Q a square? [#permalink]

25 Sep 2019, 00:56

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Just to be a bit more clearer to learners like myself - Rhombuses DONT have diagonals of equal length.

If the diagonals of a parallelogram are of equal length then the shape is a rectangle or square.

So if the diagonals of a rhombus are equal then the shape is a square.

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Hoozan

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Re: Is quadrilateral Q a square? [#permalink]

05 Feb 2022, 05:23

Parallelogram is a "parent" of some other quadrilaterals

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Re: Is quadrilateral Q a square? [#permalink]

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Re: Is quadrilateral Q a square? [#permalink]

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