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

It is currently 24 Jun 2018, 07:48

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

Arc ABC is a semicircle. The perimeter of region ABC is x.

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

Hide Tags

1 KUDOS received
Intern
Intern
avatar
Joined: 08 Oct 2011
Posts: 39
GMAT ToolKit User
Arc ABC is a semicircle. The perimeter of region ABC is x. [#permalink]

Show Tags

New post Updated on: 29 Sep 2013, 11:28
1
2
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

61% (01:28) correct 39% (01:26) wrong based on 175 sessions

HideShow timer Statistics

Attachment:
Untitled.png
Untitled.png [ 891 Bytes | Viewed 6874 times ]
Arc ABC is a semicircle. The perimeter of region ABC is x. What is the area of region ABC in terms of x?

A. \(\frac{\pi{x^2}}{8(2+\pi)^2}\)

B. \(\frac{x^2}{64}\)

C. \(\frac{\pi{x^2}}{2(2+\pi)^2}\)

D. \(\frac{\pi{x^2}}{(2+\pi)^2}\)

E. \(\frac{\pi{x^2}}{(4+\pi)^2}\)

Attachment:
Screen Shot 2013-09-29 at 5.38.24 PM.png
Screen Shot 2013-09-29 at 5.38.24 PM.png [ 23.76 KiB | Viewed 6023 times ]


My approach to the question:

If ABC is a semicircle with circumference x, then (2πr)/2=x
πr=x, r=x/π

Area of the circle = 1/2 π r^2 = 1/2 π (x/π) ^ 2 = x^2/2π

Unfortunately, I did not see any such answer option hence randomly picked C. Where did I go wrong in the calculation? Expert opinion appreciated.

Originally posted by aakrity on 29 Sep 2013, 05:22.
Last edited by Bunuel on 29 Sep 2013, 11:28, edited 1 time in total.
Edited the question.
VP
VP
User avatar
Status: Been a long time guys...
Joined: 03 Feb 2011
Posts: 1271
Location: United States (NY)
Concentration: Finance, Marketing
GPA: 3.75
GMAT ToolKit User Premium Member
Re: Arc ABC is a semicircle [#permalink]

Show Tags

New post 29 Sep 2013, 06:04
aakrity wrote:
Arc ABC is a semicircle. The perimeter of region ABC is x. What is the area of region ABC in terms of x?

U didn't take the diameter of the semicircle.
On taking the diameter of the semi-circle, the radius in terms of x would come out as r=x/(2+pi).
Rest is simple.
Area=pi*r^2/2.
Hence +1C
_________________

Prepositional Phrases Clarified|Elimination of BEING| Absolute Phrases Clarified
Rules For Posting
www.Univ-Scholarships.com

Intern
Intern
avatar
Joined: 08 Oct 2011
Posts: 39
GMAT ToolKit User
Re: Arc ABC is a semicircle [#permalink]

Show Tags

New post 29 Sep 2013, 06:21
Marcab wrote:
aakrity wrote:
Arc ABC is a semicircle. The perimeter of region ABC is x. What is the area of region ABC in terms of x?

U didn't take the diameter of the semicircle.
On taking the diameter of the semi-circle, the radius in terms of x would come out as r=x/(2+pi).
Rest is simple.
Area=pi*r^2/2.
Hence +1C


Thanks for your response but this is where the Kaplan explanation got me. Isn't the circumference / perimeter of the circle 2πr only? Hence, πr for a semi circle.
Expert Post
2 KUDOS received
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 46307
Re: Arc ABC is a semicircle. The perimeter of region ABC is x. [#permalink]

Show Tags

New post 29 Sep 2013, 11:27
2
Image
Arc ABC is a semicircle. The perimeter of region ABC is x. What is the area of region ABC in terms of x?

A. \(\frac{\pi{x^2}}{8(2+\pi)^2}\)

B. \(\frac{x^2}{64}\)

C. \(\frac{\pi{x^2}}{2(2+\pi)^2}\)

D. \(\frac{\pi{x^2}}{(2+\pi)^2}\)

E. \(\frac{\pi{x^2}}{(4+\pi)^2}\)

The perimeter of region ABC is half of the circumference (arc ABC) + the diameter of the circle (AC) = \(\frac{2\pi{r}}{2}+2r=x\) --> \(r=\frac{x}{\pi+2}\).

The area of the semicircle = \(\frac{\pi{r^2}}{2}=\frac{\pi{x^2}}{2(\pi+2)^2}\).

Answer: C.

Hope it's clear.
_________________

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

Senior Manager
Senior Manager
avatar
G
Joined: 26 Dec 2015
Posts: 277
Location: United States (CA)
Concentration: Finance, Strategy
WE: Investment Banking (Venture Capital)
Re: Arc ABC is a semicircle. The perimeter of region ABC is x. [#permalink]

Show Tags

New post 27 Feb 2017, 18:06
is there any way of solving this by plugging in #s (ex: for the radius?)
Re: Arc ABC is a semicircle. The perimeter of region ABC is x.   [#permalink] 27 Feb 2017, 18:06
Display posts from previous: Sort by

Arc ABC is a semicircle. The perimeter of region ABC is x.

  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®.