The area of each of the 16 square regions in the figure abov : Problem Solving (PS)

My Profile Logout

Test's Subscription Expires:

My Follow Feed Kudos My Error Log

Messages and Replies

Settings Mark All Read

See All

Applicant Notifications

Settings Mark All Read

See All

Global notifications

Settings Mark All Read

See All

The area of each of the 16 square regions in the figure abov

Sort by Date

Sort by Kudos

Author

Message

TAGS:

Hide Tags

Director

Joined: 29 Nov 2012

Posts: 759

The area of each of the 16 square regions in the figure abov [#permalink]

Show Tags

Updated on: 09 Sep 2013, 23:55

00:00

Difficulty:

35% (medium)

Question Stats:

75% (01:53) correct

25% (02:00) wrong

based on 357 sessions

HideShow timer Statistics

Attachment:

Untitled.png [ 24.67 KiB | Viewed 5658 times ]

The area of each of the 16 square regions in the figure above is T. What is the area of the shaded region?

A. \(\frac{13T}{3}\)

B. \(5T\)

C. \(\frac{16T}{3}\)

D. \(\frac{11T}{2}\)

E. \(7T\)

Spoiler: ::

Please provide detailed explanations!

Spoiler: OA

Originally posted by fozzzy on 09 Sep 2013, 23:30.
Last edited by Bunuel on 09 Sep 2013, 23:55, edited 1 time in total.

Edited the question.

Most Helpful Expert Reply

Math Expert

Joined: 02 Sep 2009

Posts: 51280

Re: The area of each of the 16 square regions in the figure abov [#permalink]

Show Tags

10 Sep 2013, 00:03

fozzzy wrote:

The area of each of the 16 square regions in the figure above is T. What is the area of the shaded region?

A. \(\frac{13T}{3}\)

B. \(5T\)

C. \(\frac{16T}{3}\)

D. \(\frac{11T}{2}\)

E. \(7T\)

Spoiler: ::

Please provide detailed explanations!

The whole area = 16T.

The areas of three unshaded triangles are = T + 6T + 4T = 11T (half of a rectangle with area of 2 + half of a rectangle with area of 12 + half of a rectangle with area of 8).

The area of the shaded region = 16T - 11T = 5T.

Answer: B.

Similar question to practice: what-is-the-area-of-a-triangle-with-the-following-vertices-125983.html
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.

What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

General Discussion

Director

Joined: 29 Nov 2012

Posts: 759

Re: The area of each of the 16 square regions in the figure abov [#permalink]

Show Tags

Updated on: 10 Sep 2013, 04:27

So basically what you have done is count the squares and calculated the area's I have modified the image and added color ( Red,Black and blue) so

Black has 4*2*1/2
Red has 4*3*1/2
Blue has 2*1*1/2

is this correct and then subtract from the total?

Attachments

image modified.png [ 21.29 KiB | Viewed 5047 times ]

Originally posted by fozzzy on 10 Sep 2013, 00:21.
Last edited by fozzzy on 10 Sep 2013, 04:27, edited 1 time in total.

Math Expert

Joined: 02 Sep 2009

Posts: 51280

Re: The area of each of the 16 square regions in the figure abov [#permalink]

Show Tags

10 Sep 2013, 00:23

fozzzy wrote:

So basically what you have done is count the squares and took the area's I have modified the image and added color ( Red,Black and blue) so

Black has 4*2*1/2
Red has 4*3*1/2
Blue has 2*1*1/2

is this correct and then subtract from the total?

Yes, that's correct.
_________________

Manager

Joined: 07 May 2013

Posts: 97

Re: The area of each of the 16 square regions in the figure abov [#permalink]

Show Tags

19 Nov 2013, 22:05

16T-[(\(\frac{1}{2}\)*2\(\sqrt{T}\)*\(\sqrt{T}\))+(\(\frac{1}{2}\)*4\(\sqrt{T}\)*3\(\sqrt{T}\))+(\(\frac{1}{2}\)*2\(\sqrt{T}\)*4\(\sqrt{T}\))] = 5T

Intern

Joined: 07 Feb 2011

Posts: 13

GMAT 1: 580 Q47 V24

Re: The area of each of the 16 square regions in the figure abov [#permalink]

Show Tags

07 Mar 2014, 06:43

Bunuel.. can you please elaborate on "The areas of three unshaded triangles are = T + 6T + 4T = 11T (half of a rectangle with area of 2 + half of a rectangle with area of 12 + half of a rectangle with area of 8)."
I not able to follow this part.

Manager

Joined: 20 Dec 2013

Posts: 230

Location: India

Re: The area of each of the 16 square regions in the figure abov [#permalink]

Show Tags

07 Mar 2014, 16:58

Option B.
Let T be any convenient no. say 36.
Side of each smaller square=6
Side of bigger square=6*4=24
Area shaded=24^2-(area of 3 unshaded right triangles)
=576-36-144-216
=180
Which is 5*36
Ans:5T

Posted from my mobile device

Math Expert

Joined: 02 Sep 2009

Posts: 51280

Re: The area of each of the 16 square regions in the figure abov [#permalink]

Show Tags

08 Mar 2014, 04:57

satsymbol wrote:

Attachment:

Untitled.png [ 32 KiB | Viewed 4568 times ]

The areas of three unshaded triangles are =
Half of the area of blue rectangle with area of 2T , thus T;
Half of the area of black rectangle with area of 8T , thus 4T.
Half of the area of red rectangle with area of 12T , thus 6T.

T + 4T + 6T = 11T.

Hope it's clear.
_________________

Intern

Joined: 27 May 2018

Posts: 2

The area of each of the 16 square regions in the figure abov [#permalink]

Show Tags

18 Oct 2018, 08:02

fozzzy wrote:

Attachment:

Untitled.png

The area of each of the 16 square regions in the figure above is T. What is the area of the shaded region?

A. \(\frac{13T}{3}\)

B. \(5T\)

C. \(\frac{16T}{3}\)

D. \(\frac{11T}{2}\)

E. \(7T\)

Spoiler: ::

Please provide detailed explanations!

my answer is
The 2nd horizontal line divides the shape into two triangles having the same base and the same ht.

area=2*1/2* sqrt(T)*(1+1+.5)*(sqrt(T)(1+1)
=5T

Is my approach correct??
_________________

GMAT Side effects
-------------------
G-Groggy
M-Mental
A-Annoyed
T-Twit

Manager

Joined: 07 Aug 2018

Posts: 110

Location: United States (MA)

GMAT 1: 560 Q39 V28

The area of each of the 16 square regions in the figure abov [#permalink]

Show Tags

19 Oct 2018, 05:14

Rather simple, but maybe more time consuming approach is to simply estimate and count the fraction of the shaded areas in each square:

\(\frac{1}{3}+\frac{2}{3}+\frac{1}{3}+\frac{1}{3}+\frac{2}{3}+\frac{2}{3}+\frac{3}{3}+\frac{1}{3}+\frac{1}{3}+\frac{1}{3}=\frac{15}{3}=5\)
_________________

Quantitative Megathread:https://gmatclub.com/forum/ultimate-gmat-quantitative-megathread-244512.html
Verbal Megathread:https://gmatclub.com/forum/all-you-need-for-gmat-verbal-164070.html
Flashcards Quant + Verbal:https://gmatclub.com/forum/gmat-flashcards-108651.html
Thursdays with Ron:https://gmatclub.com/forum/manhattan-s-thursdays-with-ron-consolidated-video-index-223612.html#p2138753