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

It is currently 22 Jun 2018, 04:37

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

Rectangle ABCD has a perimeter of 26. The half circle with diameter AD

  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: 46280
Rectangle ABCD has a perimeter of 26. The half circle with diameter AD [#permalink]

Show Tags

New post 12 May 2016, 04:42
00:00
A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

70% (01:25) correct 30% (01:22) wrong based on 76 sessions

HideShow timer Statistics

Image
Rectangle ABCD has a perimeter of 26. The half circle with diameter AD has an area of 8π. What is the perimeter of the part of the figure that is not shaded?

A. 26 + 4π
B. 18 + 8π
C. 18 + 4π
D. 14 + 4π
E. 14 + 2π

Attachment:
2016-05-12_1536.png
2016-05-12_1536.png [ 1.99 KiB | Viewed 3019 times ]

_________________

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

SC Moderator
User avatar
D
Joined: 13 Apr 2015
Posts: 1689
Location: India
Concentration: Strategy, General Management
GMAT 1: 200 Q1 V1
GPA: 4
WE: Analyst (Retail)
GMAT ToolKit User Premium Member
Re: Rectangle ABCD has a perimeter of 26. The half circle with diameter AD [#permalink]

Show Tags

New post 12 May 2016, 06:59
(pi * r^2)/2 = 8pi
r^2 = 16
r = 4 --> Diameter = Length of the rectangle = 8

16 + 2(Width) = 26
Width = 5

Perimeter of the part of the figure thats not shaded = 8 + 10 + (2 * pi * 4)/2 = 18 + 4pi

Answer: C
DS Forum Moderator
avatar
P
Joined: 22 Aug 2013
Posts: 1209
Location: India
Premium Member
Re: Rectangle ABCD has a perimeter of 26. The half circle with diameter AD [#permalink]

Show Tags

New post 25 May 2017, 21:56
Area of half circle = πr^2/2, where r is the radius.
equating, 8π = πr^2/2, we get r^2 = 16 or r = 4.

Thus the side of the rectangle (having half circle) is 4*2 = 8. Let the other side be x.
Then perimeter = 2(8+x) = 26, this gives x=5

Perimeter of part that is not shaded = AB + BC + CD + semi circular arc

Now, AB = CD = 5, BC = 8.
Semi circular arc = 2πr/2 = πr = π*4 = 4π

Hence required perimeter = 5+5+8+4π = 18+4π

Thus answer is C
Re: Rectangle ABCD has a perimeter of 26. The half circle with diameter AD   [#permalink] 25 May 2017, 21:56
Display posts from previous: Sort by

Rectangle ABCD has a perimeter of 26. The half circle with diameter AD

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


GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| 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®.