GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 13 Dec 2018, 12:59

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Events & Promotions

Events & Promotions in December
PrevNext
SuMoTuWeThFrSa
2526272829301
2345678
9101112131415
16171819202122
23242526272829
303112345
Open Detailed Calendar
• GMATbuster's Weekly GMAT Quant Quiz, Tomorrow, Saturday at 9 AM PST

December 14, 2018

December 14, 2018

09:00 AM PST

10:00 AM PST

10 Questions will be posted on the forum and we will post a reply in this Topic with a link to each question. There are prizes for the winners.
• The winning strategy for 700+ on the GMAT

December 13, 2018

December 13, 2018

08:00 AM PST

09:00 AM PST

What people who reach the high 700's do differently? We're going to share insights, tips and strategies from data we collected on over 50,000 students who used examPAL.

M25-14

Author Message
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 51185

Show Tags

16 Sep 2014, 00:23
14
00:00

Difficulty:

75% (hard)

Question Stats:

43% (01:05) correct 57% (01:06) wrong based on 302 sessions

HideShow timer Statistics

If $$ABCD$$ is a quadrilateral, is $$AB = BC = CD = DA$$?

(1) AC is perpendicular to BD

(2) $$AB + CD = BC + AD$$

_________________
Math Expert
Joined: 02 Sep 2009
Posts: 51185

Show Tags

16 Sep 2014, 00:23
3
Official Solution:

Based on geometry, $$ABCD$$ can be a rhombus ($$AB = BC = CD = DA$$) but it can also be a kite-shaped figure whose diagonals form a cross (S1 holds). S2 holds because of the symmetry of the kite ($$AB = BC$$ and $$CD = AD$$).

_________________
Intern
Joined: 09 Mar 2014
Posts: 4
GPA: 3.01
WE: General Management (Energy and Utilities)

Show Tags

06 Dec 2014, 02:03
but if both the diagonals are perpendicular to each other (Option-1) , then it could be RHOMBUS only. then its all the sides are equal.
Which other quadilateral have perpendicular diagonals? Square ! that means it could be square also and square also has all sides equal.

Math Expert
Joined: 02 Sep 2009
Posts: 51185

Show Tags

06 Dec 2014, 05:13
6
7
manojpandey80 wrote:
but if both the diagonals are perpendicular to each other (Option-1) , then it could be RHOMBUS only. then its all the sides are equal.
Which other quadilateral have perpendicular diagonals? Square ! that means it could be square also and square also has all sides equal.

Both kite and rhombus have the diagonals perpendicular to each other and the sum of the opposite sides equal to each other. So, ABCD can be a kite or a rhombus. Look at the diagram below:

Alternative solution:
If ABCD is a quadrilateral, is AB=BC=CD=DA ?

(1) AC is perpendicular to BD. The diagonals are perpendicular to each other: ABCD could be a kite (answer NO), a rhombus (answer YES) or a square, which is just a special type of rhombus (answer YES). Not sufficient.

(2) AB+CD=BC+DA. The sum of opposite sides are equal. Clearly insufficient.

(1)+(2) ABCD could be a kite (see the diagram below) - answer NO or a square/rhombus - answer YES. Not sufficient.

_________________
Intern
Joined: 16 Jul 2015
Posts: 1

Show Tags

30 Aug 2015, 00:59
I think this is a high-quality question and the explanation isn't clear enough, please elaborate. In a rhombus all four sides are equal.
Math Expert
Joined: 02 Sep 2009
Posts: 51185

Show Tags

30 Aug 2015, 07:35
aganesh wrote:
I think this is a high-quality question and the explanation isn't clear enough, please elaborate. In a rhombus all four sides are equal.

Have you checked this post: m25-184416.html#p1451996 ?
_________________
Intern
Joined: 13 Sep 2015
Posts: 17

Show Tags

20 Sep 2015, 10:19
I think bunuel explanation is more than sufficient. Thanks. The diagrams helped. I had trouble imagining the object, but then again I suck at geometry.
Senior Manager
Joined: 31 Mar 2016
Posts: 385
Location: India
Concentration: Operations, Finance
GMAT 1: 670 Q48 V34
GPA: 3.8
WE: Operations (Commercial Banking)

Show Tags

26 Jul 2016, 10:10
I think this is a high-quality question and I agree with explanation.
Intern
Joined: 14 Nov 2015
Posts: 30
Location: India
GPA: 3.7

Show Tags

16 Dec 2017, 07:01
manojpandey80 wrote:
but if both the diagonals are perpendicular to each other (Option-1) , then it could be RHOMBUS only. then its all the sides are equal.
Which other quadilateral have perpendicular diagonals? Square ! that means it could be square also and square also has all sides equal.

Diagonals are perpendicular in parallelogram, rectangle, square and rhombus.
Math Expert
Joined: 02 Sep 2009
Posts: 51185

Show Tags

16 Dec 2017, 08:18
Ashokshiva wrote:
manojpandey80 wrote:
but if both the diagonals are perpendicular to each other (Option-1) , then it could be RHOMBUS only. then its all the sides are equal.
Which other quadilateral have perpendicular diagonals? Square ! that means it could be square also and square also has all sides equal.

Diagonals are perpendicular in parallelogram, rectangle, square and rhombus.

The diagonal in parallelogram and rectangle are NOT perpendicular to each other.

For more practice Properties of Polygons Questions.
_________________
Intern
Joined: 14 Nov 2015
Posts: 30
Location: India
GPA: 3.7

Show Tags

17 Dec 2017, 09:32
Bunuel wrote:
Ashokshiva wrote:
manojpandey80 wrote:
but if both the diagonals are perpendicular to each other (Option-1) , then it could be RHOMBUS only. then its all the sides are equal.
Which other quadilateral have perpendicular diagonals? Square ! that means it could be square also and square also has all sides equal.

Diagonals are perpendicular in parallelogram, rectangle, square and rhombus.

The diagonal in parallelogram and rectangle are NOT perpendicular to each other.

For more practice Properties of Polygons Questions.

thanks

The diagonals in parallelogram and rectangle only bisect each other and are not perpendicular.
Re: M25-14 &nbs [#permalink] 17 Dec 2017, 09:32
Display posts from previous: Sort by

M25-14

Moderators: chetan2u, Bunuel

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.