It is currently 17 Dec 2017, 15:15

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

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

In the figure above, ABCD is a rectangle and the curved path is made

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

Hide Tags

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 42652

Kudos [?]: 135981 [0], given: 12719

In the figure above, ABCD is a rectangle and the curved path is made [#permalink]

Show Tags

New post 29 Nov 2017, 21:52
00:00
A
B
C
D
E

Difficulty:

(N/A)

Question Stats:

67% (00:57) correct 33% (01:39) wrong based on 26 sessions

HideShow timer Statistics

Image
In the figure above, ABCD is a rectangle and the curved path is made up of 16 semicircles of equal diameter. If the total length of the curved path is 32π, then the area of rectangle ABCD is

(A) 24
(B) 32
(C) 48
(D) 64
(E) 192

[Reveal] Spoiler:
Attachment:
2017-11-30_0948.png
2017-11-30_0948.png [ 45.01 KiB | Viewed 428 times ]
[Reveal] Spoiler: OA

_________________

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

Kudos [?]: 135981 [0], given: 12719

Intern
Intern
User avatar
B
Joined: 15 Oct 2017
Posts: 27

Kudos [?]: 3 [0], given: 57

Location: Ireland
Concentration: Healthcare, Finance
Re: In the figure above, ABCD is a rectangle and the curved path is made [#permalink]

Show Tags

New post 29 Nov 2017, 23:01
Bunuel wrote:
Image
In the figure above, ABCD is a rectangle and the curved path is made up of 16 semicircles of equal diameter. If the total length of the curved path is 32π, then the area of rectangle ABCD is

(A) 24
(B) 32
(C) 48
(D) 64
(E) 192

[Reveal] Spoiler:
Attachment:
2017-11-30_0948.png


16 semicircles are 8 circles => \(8 * 2 \pi * r = 32 \pi\)
\(r = 2 => D = 4\)

6D * 2D = area ABCD
\(24 * 8 = 192\)
E

Kudos [?]: 3 [0], given: 57

Expert Post
e-GMAT Representative
User avatar
S
Joined: 04 Jan 2015
Posts: 755

Kudos [?]: 2252 [0], given: 123

Re: In the figure above, ABCD is a rectangle and the curved path is made [#permalink]

Show Tags

New post 30 Nov 2017, 10:57
Bunuel wrote:
Image
In the figure above, ABCD is a rectangle and the curved path is made up of 16 semicircles of equal diameter. If the total length of the curved path is 32π, then the area of rectangle ABCD is

(A) 24
(B) 32
(C) 48
(D) 64
(E) 192

[Reveal] Spoiler:
Attachment:
2017-11-30_0948.png


Let us assume the diameter of the semi-circle to be D.

From the given information, we can write :

\(16 * π* \frac{D}{2} = 32 π\)

\(D = 4\)

Now from the diagram, notice the length of the rectangle \(= 6*D = 6*4 = 24\)

And the breadth of the rectangle \(= 2D = 2 * 4 = 8\)

Thus, the area of the rectangle \(= L *B = 24 * 8 = 192\)

The correct answer is Option E.
_________________












| '4 out of Top 5' Instructors on gmatclub | 70 point improvement guarantee | www.e-gmat.com

Kudos [?]: 2252 [0], given: 123

Manager
Manager
avatar
B
Joined: 01 Feb 2017
Posts: 60

Kudos [?]: 19 [0], given: 20

In the figure above, ABCD is a rectangle and the curved path is made [#permalink]

Show Tags

New post 02 Dec 2017, 13:40
There are 16 semi-circles along the perimeter of the rectangle.

This equals to 8 circles with total circumference of 32π

So, Circumference of each circle is 4π

This equals to diameter per circle of 4 units.

So, In the Rectangle, There are six diameters along the length equaling 24 units and two diameters along width equaling 8 units.

Therefore, Area of Rectangle is 24*8 = 192 sq. Units

Ans E

Posted from my mobile device

Kudos [?]: 19 [0], given: 20

Expert Post
Target Test Prep Representative
User avatar
S
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 1945

Kudos [?]: 1024 [0], given: 3

Location: United States (CA)
Re: In the figure above, ABCD is a rectangle and the curved path is made [#permalink]

Show Tags

New post 03 Dec 2017, 17:56
Bunuel wrote:
Image
In the figure above, ABCD is a rectangle and the curved path is made up of 16 semicircles of equal diameter. If the total length of the curved path is 32π, then the area of rectangle ABCD is

(A) 24
(B) 32
(C) 48
(D) 64
(E) 192

[Reveal] Spoiler:
Attachment:
2017-11-30_0948.png


Since the curved path is made up of 16 semicircles, each semicircular arc is 32π/16 = 2π. Thus, the diameter of each semicircle is 4 (notice that ½ x 4π = 2π). Since the length of the rectangle is made up of 6 diameters, the length = 24, and, since the width is made up of 2 diameters, the width = 8, so the area is 24 x 8 = 192.

Answer: E
_________________

Scott Woodbury-Stewart
Founder and CEO

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Kudos [?]: 1024 [0], given: 3

Re: In the figure above, ABCD is a rectangle and the curved path is made   [#permalink] 03 Dec 2017, 17:56
Display posts from previous: Sort by

In the figure above, ABCD is a rectangle and the curved path is made

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


GMAT Club MBA Forum Home| About| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

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

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.