It is currently 21 Oct 2017, 18:13

### 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 June
Open Detailed Calendar

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

Author Message
TAGS:

### Hide Tags

Current Student
Joined: 25 Sep 2012
Posts: 287

Kudos [?]: 174 [4], given: 242

Location: India
Concentration: Strategy, Marketing
GMAT 1: 660 Q49 V31
GMAT 2: 680 Q48 V34
In the figure given below, ABCD is a square, and P, Q, R and [#permalink]

### Show Tags

03 Oct 2013, 02:12
4
KUDOS
10
This post was
BOOKMARKED
00:00

Difficulty:

45% (medium)

Question Stats:

69% (01:42) correct 31% (01:47) wrong based on 215 sessions

### HideShow timer Statistics

Attachment:

tS6VTJ2.jpg [ 11.04 KiB | Viewed 4855 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
[Reveal] Spoiler: OA

Kudos [?]: 174 [4], given: 242

Math Expert
Joined: 02 Sep 2009
Posts: 41892

Kudos [?]: 129171 [1], given: 12194

Re: In the figure given below, ABCD is a square, and P, Q, R and [#permalink]

### Show Tags

03 Oct 2013, 02:27
1
KUDOS
Expert's post
1
This post was
BOOKMARKED
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 [ 30.11 KiB | Viewed 4832 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.

The ratio for the entire square would be the same.

_________________

Kudos [?]: 129171 [1], given: 12194

Current Student
Joined: 25 Sep 2012
Posts: 287

Kudos [?]: 174 [0], given: 242

Location: India
Concentration: Strategy, Marketing
GMAT 1: 660 Q49 V31
GMAT 2: 680 Q48 V34
Re: In the figure given below, ABCD is a square, and P, Q, R and [#permalink]

### Show Tags

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.

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...

Kudos [?]: 174 [0], given: 242

Manager
Joined: 07 May 2013
Posts: 108

Kudos [?]: 30 [0], given: 1

Re: In the figure given below, ABCD is a square, and P, Q, R and [#permalink]

### Show Tags

18 Nov 2013, 19:39
1
This post was
BOOKMARKED
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.

Kudos [?]: 30 [0], given: 1

Director
Joined: 25 Apr 2012
Posts: 724

Kudos [?]: 847 [0], given: 724

Location: India
GPA: 3.21
Re: In the figure given below, ABCD is a square, and P, Q, R and [#permalink]

### Show Tags

19 Nov 2013, 04:17
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
_________________

“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.”

Kudos [?]: 847 [0], given: 724

Senior Manager
Joined: 23 Apr 2015
Posts: 332

Kudos [?]: 113 [0], given: 36

Location: United States
WE: Engineering (Consulting)
Re: In the figure given below, ABCD is a square, and P, Q, R and [#permalink]

### Show Tags

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

Kudos [?]: 113 [0], given: 36

GMAT Club Legend
Joined: 09 Sep 2013
Posts: 16587

Kudos [?]: 273 [0], given: 0

Re: In the figure given below, ABCD is a square, and P, Q, R and [#permalink]

### Show Tags

03 Oct 2017, 09:20
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.
_________________

Kudos [?]: 273 [0], given: 0

Re: In the figure given below, ABCD is a square, and P, Q, R and   [#permalink] 03 Oct 2017, 09:20
Display posts from previous: Sort by