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

It is currently 14 Dec 2019, 08:21

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

In the figure given below, ABCD is a square, and P, Q, R and

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

Hide Tags

Find Similar Topics 
Manager
Manager
User avatar
Joined: 25 Sep 2012
Posts: 228
Location: India
Concentration: Strategy, Marketing
GMAT 1: 660 Q49 V31
GMAT 2: 680 Q48 V34
GMAT ToolKit User Reviews Badge
In the figure given below, ABCD is a square, and P, Q, R and  [#permalink]

Show Tags

New post 03 Oct 2013, 02:12
5
23
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

64% (02:12) correct 36% (02:01) wrong based on 318 sessions

HideShow timer Statistics

Attachment:
tS6VTJ2.jpg
tS6VTJ2.jpg [ 11.04 KiB | Viewed 18841 times ]

In the figure given below, ABCD is a square, and P, Q, R and S are the mid-points of the sides AB, BC, CD and AD respectively. The ratio of the area of the shaded region to the area of the square ABCD is

A. 1/3
B. 1/4
C. 1/5
D. 1/6
E. 1/8
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 59725
Re: In the figure given below, ABCD is a square, and P, Q, R and  [#permalink]

Show Tags

New post 03 Oct 2013, 02:27
1
1
b2bt wrote:
Attachment:
The attachment tS6VTJ2.jpg is no longer available

In the figure given below, ABCD is a square, and P, Q, R and S are the mid-points of the sides AB, BC, CD and AD respectively. The ratio of the area of the shaded region to the area of the square ABCD is

A. 1/3
B. 1/4
C. 1/5
D. 1/6
E. 1/8


Attachment:
Untitled.png
Untitled.png [ 30.11 KiB | Viewed 18775 times ]

Consider square APNS and say its side is 1. In this case:

The area of APNS is 1.
MN = 1/2, which means that the area of SMN is 1/2*1/2*1=1/4.

(shaded)/(square)=(1/4)/1=1/4.

The ratio for the entire square would be the same.

Answer: B.
_________________
Manager
Manager
User avatar
Joined: 25 Sep 2012
Posts: 228
Location: India
Concentration: Strategy, Marketing
GMAT 1: 660 Q49 V31
GMAT 2: 680 Q48 V34
GMAT ToolKit User Reviews Badge
Re: In the figure given below, ABCD is a square, and P, Q, R and  [#permalink]

Show Tags

New post 03 Oct 2013, 03:08
Bunuel wrote:
b2bt wrote:
Attachment:
tS6VTJ2.jpg

In the figure given below, ABCD is a square, and P, Q, R and S are the mid-points of the sides AB, BC, CD and AD respectively. The ratio of the area of the shaded region to the area of the square ABCD is

A. 1/3
B. 1/4
C. 1/5
D. 1/6
E. 1/8


Attachment:
Untitled.png

Consider square APNS and say its side is 1. In this case:

The area of APNS is 1.
MN = 1/2, which means that the area of SMN is 1/2*1/2*1=1/4.

(shaded)/(square)=(1/4)/1=1/4.

The ratio for the entire square would be the same.

Answer: B.



How did you get MN as half? I solved the same way but assumed it to half...
Manager
Manager
avatar
Joined: 07 May 2013
Posts: 87
Re: In the figure given below, ABCD is a square, and P, Q, R and  [#permalink]

Show Tags

New post 18 Nov 2013, 19:39
1
APNS is a square. It's side is 1(as assumed by buneul). This means that ABQS is a rectangle with AS=1 and SQ=2. Hence, PN=1. SB and AQ are diagonals of the rectangle. Let them meet at the point M. Draw an imaginary line say XY passing through M and parallel to both AB and SQ. Now observe that PN bisects SQ that is SN=NQ=1. This implies that XY passing through M should also bisect AS, PN and BQ. Therefore, MN=1/2. This property holds good for all rectangles.
Director
Director
User avatar
Joined: 25 Apr 2012
Posts: 651
Location: India
GPA: 3.21
WE: Business Development (Other)
Reviews Badge
Re: In the figure given below, ABCD is a square, and P, Q, R and  [#permalink]

Show Tags

New post 19 Nov 2013, 04:17
1
b2bt wrote:
Bunuel wrote:
b2bt wrote:
Attachment:
tS6VTJ2.jpg

In the figure given below, ABCD is a square, and P, Q, R and S are the mid-points of the sides AB, BC, CD and AD respectively. The ratio of the area of the shaded region to the area of the square ABCD is

A. 1/3
B. 1/4
C. 1/5
D. 1/6
E. 1/8


Attachment:
Untitled.png

Consider square APNS and say its side is 1. In this case:

The area of APNS is 1.
MN = 1/2, which means that the area of SMN is 1/2*1/2*1=1/4.


(shaded)/(square)=(1/4)/1=1/4.

The ratio for the entire square would be the same.

Answer: B.



How did you get MN as half? I solved the same way but assumed it to half...



Hello B2bt,

Consider triangle SMN and SBQ

Angles S is common
Angle N is equal to Angle Q and
Angle M is equal to angle B

Since the triangles are similar therefore MN=1/2BQ ie. 1/2
_________________

“If you can't fly then run, if you can't run then walk, if you can't walk then crawl, but whatever you do you have to keep moving forward.”
Senior Manager
Senior Manager
avatar
Joined: 23 Apr 2015
Posts: 279
Location: United States
Concentration: General Management, International Business
WE: Engineering (Consulting)
Re: In the figure given below, ABCD is a square, and P, Q, R and  [#permalink]

Show Tags

New post 12 Sep 2016, 10:09
b2bt wrote:
Attachment:
tS6VTJ2.jpg

In the figure given below, ABCD is a square, and P, Q, R and S are the mid-points of the sides AB, BC, CD and AD respectively. The ratio of the area of the shaded region to the area of the square ABCD is

A. 1/3
B. 1/4
C. 1/5
D. 1/6
E. 1/8


The figure can be seen as four identical squares with identical shaded region and each individual square. And the shaded region is from one end to the mid point of the other corner. This means it's 1/4 of the area of the main square. Since these are identical, the Answer is B) 1/4
Senior Manager
Senior Manager
User avatar
G
Joined: 29 Dec 2017
Posts: 373
Location: United States
Concentration: Marketing, Technology
GMAT 1: 630 Q44 V33
GMAT 2: 690 Q47 V37
GMAT 3: 710 Q50 V37
GPA: 3.25
WE: Marketing (Telecommunications)
In the figure given below, ABCD is a square, and P, Q, R and  [#permalink]

Show Tags

New post Updated on: 21 Sep 2018, 06:25
Since the answer choices are quite far from one another, the best way for such graphical problems is approximation.
We have got 4 right triangles, which you can easily fit into one of the small triangle (1/4 of original one). Hence the ratio is 1:4. Time taken 47 sec.

Originally posted by Hero8888 on 22 Aug 2018, 07:18.
Last edited by Hero8888 on 21 Sep 2018, 06:25, edited 1 time in total.
CEO
CEO
User avatar
D
Status: GMATINSIGHT Tutor
Joined: 08 Jul 2010
Posts: 2977
Location: India
GMAT: INSIGHT
Schools: Darden '21
WE: Education (Education)
Reviews Badge
Re: In the figure given below, ABCD is a square, and P, Q, R and  [#permalink]

Show Tags

New post 20 Sep 2018, 21:54
b2bt wrote:
Attachment:
The attachment tS6VTJ2.jpg is no longer available

In the figure given below, ABCD is a square, and P, Q, R and S are the mid-points of the sides AB, BC, CD and AD respectively. The ratio of the area of the shaded region to the area of the square ABCD is

A. 1/3
B. 1/4
C. 1/5
D. 1/6
E. 1/8


In such question Most important part is to break the shaded portion into a few recognizable figures like I have broken as shown in figure attached

Answer: Option B
Attachments

File comment: www.GMATinsight.com
Screen Shot 2018-09-21 at 10.16.34 AM.png
Screen Shot 2018-09-21 at 10.16.34 AM.png [ 359.56 KiB | Viewed 3130 times ]


_________________
Prosper!!!
GMATinsight
Bhoopendra Singh and Dr.Sushma Jha
e-mail: info@GMATinsight.com I Call us : +91-9999687183 / 9891333772
Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi
http://www.GMATinsight.com/testimonials.html

ACCESS FREE GMAT TESTS HERE:22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION
Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 13737
Re: In the figure given below, ABCD is a square, and P, Q, R and  [#permalink]

Show Tags

New post 20 Oct 2019, 03:52
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: In the figure given below, ABCD is a square, and P, Q, R and   [#permalink] 20 Oct 2019, 03:52
Display posts from previous: Sort by

In the figure given below, ABCD is a square, and P, Q, R and

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





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