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Is the quadrilateral a square?

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Is the quadrilateral a square? [#permalink] New post 11 Feb 2012, 13:08
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Attachment:
ABCD.png
ABCD.png [ 10.14 KiB | Viewed 2121 times ]
Is quadrilateral ABCD a square?

(1) AB = BC = CD = DA
(2) AC = BD

In this question - How come the answer is C?

In Square the diagonals bisect each other at 90 degrees and are equal. How do we know that diagonals are bisecting each other at 90 degrees?
[Reveal] Spoiler: OA

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Last edited by Bunuel on 11 Feb 2012, 13:49, edited 2 times in total.
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Re: Is the quadrilateral a square? [#permalink] New post 11 Feb 2012, 13:48
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Attachment:
ABCD.png
ABCD.png [ 10.14 KiB | Viewed 2112 times ]
Is quadrilateral ABCD a square?

(1) AB = BC = CD = DA --> both square and rhombus have all four sides equal in length. Not sufficient.

(2) AC = BD --> both square and rectangle have diagonals equal in length. Not sufficient.

(1)+(2) ABCD is a square. Sufficient.

Answer: C.

Useful property: if the diagonals of a rhombus are equal, then that rhombus must be a square. So you can apply this for (1)+(2) and conclude that ABCD must be a square.

Check Polygons chapter of Math Book for more useful properties and tips: math-polygons-87336.html

Hope it helps.
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Re: Is the quadrilateral a square? [#permalink] New post 25 May 2013, 03:41
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Re: Is the quadrilateral a square? [#permalink] New post 05 Aug 2013, 18:07
from 1 it is clear that it is either a rhombus or a square as all sides are equal.

from 2 it is established that it is a square as IN A RHOMBUS DIAGONALS ARE NOT EQUAL.

hence C.
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Re: Is the quadrilateral a square? [#permalink] New post 05 Aug 2013, 22:08
enigma123 wrote:
Attachment:
ABCD.png
Is quadrilateral ABCD a square?

(1) AB = BC = CD = DA
(2) AC = BD

In this question - How come the answer is C?

In Square the diagonals bisect each other at 90 degrees and are equal. How do we know that diagonals are bisecting each other at 90 degrees?



square has equal sides and equal diagonals.
rhombus has equal sides but not equal diagonals.
so both together are sufficient...... Answer (C)

About the 2nd question, let p the point of intersection ofthe two diagonal AC and BD.
now angle PAB = angle PBA [because PA=PB]
so angle APB has to be 90 or it will not be possible for the total angle surrounding the point P to be 360.
so diagonals have to bisect at 90 degress
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Re: Is the quadrilateral a square? [#permalink] New post 30 Mar 2015, 04:35
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Is quadrilateral ABCD a square? [#permalink] New post 24 Jul 2015, 01:19
Is quadrilateral ABCD a square?

(1) AB = BC = CD = DA
(2) AC = BD
Attachments

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ABCDsquare_q.png [ 10.14 KiB | Viewed 262 times ]

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Re: Is quadrilateral ABCD a square? [#permalink] New post 24 Jul 2015, 01:23
divyarathi15 wrote:
Is quadrilateral ABCD a square?

(1) AB = BC = CD = DA
(2) AC = BD



Hi,
1) statement tells us all sides are equal. it could be a rhombus , a square etc.... insuff
2) stat 2 tells us that the diagonals are equal.. it could be a rectangle , a square or any other quad.. insuff

combined we know it can only be a square... suff
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Re: Is quadrilateral ABCD a square? [#permalink] New post 24 Jul 2015, 01:32
Hi!

We could also say from statement 1 that it could be any irregular quadrilateral (apart from being either a rhombus/sq). Again from statement 2 it can be concluded that the figure could be any irregular quad too. combining both cant it be concluded that the figure could be an irregular quadrilateral too?
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Re: Is the quadrilateral a square? [#permalink] New post 24 Jul 2015, 01:33
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Re: Is the quadrilateral a square? [#permalink] New post 24 Jul 2015, 01:40
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divyarathi15 wrote:
Is quadrilateral ABCD a square?

(1) AB = BC = CD = DA
(2) AC = BD


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Hope it helps.
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NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis ; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) ; 12. Tricky questions from previous years.

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: Is the quadrilateral a square?   [#permalink] 24 Jul 2015, 01:40
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