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

It is currently 21 Oct 2019, 06:23

Close

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
Your Progress

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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

The figure above shows four pieces of tile that have been glued togeth

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Find Similar Topics 
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 58419
The figure above shows four pieces of tile that have been glued togeth  [#permalink]

Show Tags

New post 11 Dec 2014, 07:21
1
3
00:00
A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

75% (01:31) correct 25% (02:05) wrong based on 131 sessions

HideShow timer Statistics

Tough and Tricky questions: Geometry.



Image
The figure above shows four pieces of tile that have been glued together to form a square tile ABCD. Is PR=QS?

(1) BQ = CR = DS = AP
(2) The perimeter of ABCD is 16.


Kudos for a correct solution.

Attachment:
2014-12-11_1820.png
2014-12-11_1820.png [ 4.3 KiB | Viewed 3081 times ]

_________________
Manager
Manager
User avatar
B
Joined: 18 Jun 2014
Posts: 79
Location: India
GMAT 1: 720 Q50 V38
GMAT 2: 740 Q50 V40
GPA: 3.8
WE: Business Development (Insurance)
GMAT ToolKit User Reviews Badge
Re: The figure above shows four pieces of tile that have been glued togeth  [#permalink]

Show Tags

New post 11 Dec 2014, 09:40
1
In the Figure, From option A if we consider BQ=CR=DS=AP and project their mirror images on the opposite sides, then we would obtain four isosclese Right angled triangles at the four vertices. Now, further, for PR and QS , their perpendicular lengths are equal , and since we have projected the given four lengths on their opposite sides, therefore the BASES of the two triangles are also equal (the triangles which are formed by taking PR and OS as their hypotenuse and whose base is obtained by drawing a perpendicular side from the top vertex on the opposite side) .

Hence , since base and perpendicular lengths of the two triangles are equal, so that the sides PR and QS are equal in length taking Statement A as true.

And Statement B is clearly insufficient. :) option A is the appropriate choice.
_________________
The Mind is everything . What you think you become. - Lord Buddha

Consider giving KUDOS if you appreciate my post !!
Manager
Manager
avatar
Joined: 21 Sep 2012
Posts: 207
Location: United States
Concentration: Finance, Economics
Schools: CBS '17
GPA: 4
WE: General Management (Consumer Products)
Re: The figure above shows four pieces of tile that have been glued togeth  [#permalink]

Show Tags

New post 12 Dec 2014, 01:03
statement 1 : BQ = CR = DS = AP

since ABCD is square, and BD=CR=DS=AP, then CQ=DR=AS=PB.
Not sufficient to answer whether PR=QS

statement 2 : The perimeter of ABCD is 16.

Doesn't help to answer whether PR=QS

1+2 combined, still not sufficient.

Ans = E
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 58419
Re: The figure above shows four pieces of tile that have been glued togeth  [#permalink]

Show Tags

New post 26 Dec 2014, 09:39
Manager
Manager
avatar
Joined: 05 Aug 2013
Posts: 89
Location: India
WE: Information Technology (Computer Software)
Re: The figure above shows four pieces of tile that have been glued togeth  [#permalink]

Show Tags

New post 27 Dec 2014, 01:42
Bunuel wrote:
Bunuel wrote:

Tough and Tricky questions: Geometry.



Image
The figure above shows four pieces of tile that have been glued together to form a square tile ABCD. Is PR=QS?

(1) BQ = CR = DS = AP
(2) The perimeter of ABCD is 16.


Kudos for a correct solution.

Attachment:
2014-12-11_1820.png


The correct answer is A.



Bunuel Can you please give OE for this question?


Thanks
AK
Current Student
User avatar
P
Joined: 02 Jul 2017
Posts: 289
Concentration: Entrepreneurship, Technology
GMAT 1: 730 Q50 V38
GMAT ToolKit User
The figure above shows four pieces of tile that have been glued togeth  [#permalink]

Show Tags

New post 01 Aug 2017, 04:16
1
Really tricky question,

Initially marked answer E, as got all sides of quadrilateral formed inside equal but have no detail about diagonals.

But after read that correct option is A, came up with below solution. Seems it was an easy one.

Easy and simple steps, but to explain, i have written everything in detail.

Attached the hand drawn image.

Solution:
Given Final image is a square. SO all sides are equal

Taking point 1:
BQ=CR=DS=AP = a (suppose)
let remaining portion of side = b
So total square side =a+b

Draw perpendicular from Q on AD => QE . So QE = side of square= a+b

same way Draw perpendicular from P on CD => PF . So PF = side of square= a+b

Now, as its square, all vertices are 90 degree. As BE perpendicular on AD => BQ=AE =a and BA=QE= a+b
As AD= a+b and now AE=a and given SD=a there fore ES = a+b -a -a = b-a

So right triangle triangle QES has 1 side QE=a+b and 2nd side ES=b-a. So we can find hypotenuse QS .................(1)

Same way PFR makes a right triangle with 1 side PF= a+b and 2nd side RF= b-a. So we can find hypotenuse PR ...................(2)

By above 2 equations (1) and (2),

both triangles have same sides so hypotenuse length will be same

There for PR = QS

So option 1 is sufficient.


Taking point 2:

Given side of square =16. Doesn't give us any information

So option 2 not sufficient


Answer = A


Hope above explanation makes sense.
Attachments

Geomtery question.jpg
Geomtery question.jpg [ 1.22 MiB | Viewed 1417 times ]

Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 13349
Re: The figure above shows four pieces of tile that have been glued togeth  [#permalink]

Show Tags

New post 29 Sep 2018, 06:14
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
GMAT Club Bot
Re: The figure above shows four pieces of tile that have been glued togeth   [#permalink] 29 Sep 2018, 06:14
Display posts from previous: Sort by

The figure above shows four pieces of tile that have been glued togeth

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  





Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne