Last visit was: 25 Jul 2024, 08:40 It is currently 25 Jul 2024, 08:40
Toolkit
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
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

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

SORT BY:
Tags:
Show Tags
Hide Tags
Manager
Joined: 25 Sep 2012
Posts: 203
Own Kudos [?]: 567 [57]
Given Kudos: 242
Location: India
Concentration: Strategy, Marketing
GMAT 1: 660 Q49 V31
GMAT 2: 680 Q48 V34
Math Expert
Joined: 02 Sep 2009
Posts: 94614
Own Kudos [?]: 643814 [11]
Given Kudos: 86753
General Discussion
Manager
Joined: 25 Sep 2012
Posts: 203
Own Kudos [?]: 567 [0]
Given Kudos: 242
Location: India
Concentration: Strategy, Marketing
GMAT 1: 660 Q49 V31
GMAT 2: 680 Q48 V34
Manager
Joined: 07 May 2013
Posts: 67
Own Kudos [?]: 61 [1]
Given Kudos: 1
Re: In the figure given below, ABCD is a square, and P, Q, R and [#permalink]
1
Bookmarks
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
Joined: 25 Apr 2012
Posts: 529
Own Kudos [?]: 2323 [1]
Given Kudos: 740
Location: India
GPA: 3.21
Re: In the figure given below, ABCD is a square, and P, Q, R and [#permalink]
1
Kudos
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.

The ratio for the entire square would be the same.

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
Manager
Joined: 23 Apr 2015
Posts: 234
Own Kudos [?]: 521 [1]
Given Kudos: 36
Location: United States
WE:Engineering (Consulting)
Re: In the figure given below, ABCD is a square, and P, Q, R and [#permalink]
1
Kudos
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
Joined: 29 Dec 2017
Posts: 302
Own Kudos [?]: 311 [0]
Given Kudos: 273
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]
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.
GMAT Club Legend
Joined: 08 Jul 2010
Status:GMAT/GRE Tutor l Admission Consultant l On-Demand Course creator
Posts: 6036
Own Kudos [?]: 13830 [1]
Given Kudos: 125
Location: India
GMAT: QUANT+DI EXPERT
Schools: IIM (A) ISB '24
GMAT 1: 750 Q51 V41
WE:Education (Education)
Re: In the figure given below, ABCD is a square, and P, Q, R and [#permalink]
1
Kudos
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

Attachments

File comment: www.GMATinsight.com

Screen Shot 2018-09-21 at 10.16.34 AM.png [ 359.56 KiB | Viewed 15192 times ]

GMAT Club Legend
Joined: 08 Jul 2010
Status:GMAT/GRE Tutor l Admission Consultant l On-Demand Course creator
Posts: 6036
Own Kudos [?]: 13830 [3]
Given Kudos: 125
Location: India
GMAT: QUANT+DI EXPERT
Schools: IIM (A) ISB '24
GMAT 1: 750 Q51 V41
WE:Education (Education)
Re: In the figure given below, ABCD is a square, and P, Q, R and [#permalink]
2
Kudos
1
Bookmarks
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

VP
Joined: 11 Aug 2020
Posts: 1245
Own Kudos [?]: 208 [0]
Given Kudos: 332
Re: In the figure given below, ABCD is a square, and P, Q, R and [#permalink]
Am I guilty? It is easily recognizable that the shaded region makes up 1/4 of the square. Each smaller triangle makes up 1/4 of 1/4 of the square.

Is there a better analysis?
Non-Human User
Joined: 09 Sep 2013
Posts: 34091
Own Kudos [?]: 853 [0]
Given Kudos: 0
Re: In the figure given below, ABCD is a square, and P, Q, R and [#permalink]
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.
Re: In the figure given below, ABCD is a square, and P, Q, R and [#permalink]
Moderator:
Math Expert
94614 posts