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

It is currently 20 Aug 2018, 02:10

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

A thin piece of wire 40 meters long is cut into two pieces. One piece

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

Hide Tags

Intern
Intern
avatar
Joined: 10 Jun 2009
Posts: 29
Location: Stockholm, Sweden
A thin piece of wire 40 meters long is cut into two pieces. One piece  [#permalink]

Show Tags

New post 15 Jun 2009, 00:35
2
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

66% (01:19) correct 34% (01:36) wrong based on 154 sessions

HideShow timer Statistics

A thin piece of wire 40 meters long is cut into two pieces. One piece is used to form a circle with radius R, and the other is used to form a square. No wire is left over. Which of the following represents the total area, in square meters, of the circular and square regions in terms of R.

1) \(\pi R^2\)
2) \(\pi R^2 + 10\)
3) \(\pi R^2 + 1/4\pi^2R^2\)
4) \(\pi R^2 + (40 - 2\pi R)^2\)
5) \(\pi R^2 + (10 - 1/2\pi R)^2\)

4) or 5) is a given, I just dont see how you make the calculation necessary.


OPEN DISCUSSION OF THIS QUESTION IS HERE: https://gmatclub.com/forum/a-thin-piece ... 06671.html
Current Student
User avatar
Joined: 03 Aug 2006
Posts: 112
Location: Next to Google
Schools: Haas School of Business
Re: A thin piece of wire 40 meters long is cut into two pieces. One piece  [#permalink]

Show Tags

New post 15 Jun 2009, 01:15
2
Answer is E

Given:
40 meters long wire cut into two pieces.

Now Length of piece one = circumference of a circle with radius R = \(2\pi R\)

Length of piece two = perimeter of a square created using the remaining wire = \(40-2\pi R\)

\(\Rightarrow \text{length of each side of square} = \frac{40-2\pi R}{4}\)

\(= \frac{4(10-\frac{1}{2}\pi R)}{4}\)

\(= 10-\frac{1}{2}\pi R\)

Now
\(\text{Area of circle} = \pi R^2\)
\(\text {Area of square} = (10-\frac{1}{2}\pi R)^2\)

\(\text {Sum of the areas}=\pi R^2 + (10-\frac{1}{2}\pi R)^2\)
Manager
Manager
User avatar
Joined: 07 Jun 2009
Posts: 185
Re: A thin piece of wire 40 meters long is cut into two pieces. One piece  [#permalink]

Show Tags

New post 15 Jun 2009, 03:01
Option 'E' is correct.
_________________

"Always....Read between the lines"

Manager
Manager
avatar
Status: D-Day is on February 10th. and I am not stressed
Affiliations: American Management association, American Association of financial accountants
Joined: 12 Apr 2011
Posts: 202
Location: Kuwait
Schools: Columbia university
Re: A thin piece of wire 40 meters long is cut into two pieces. One piece  [#permalink]

Show Tags

New post 07 Jan 2012, 11:49
GREAT EXPLANATION NOOKWAY. THANK YOU
_________________

Sky is the limit

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 48044
Re: A thin piece of wire 40 meters long is cut into two pieces. One piece  [#permalink]

Show Tags

New post 22 Dec 2017, 00:09
A thin piece of wire 40 meters long is cut into two pieces. One piece is used to form a circle with radius r, and the other is used to form a square. No wire is left over. Which of the following represents the total area, in square meters, of the circular and the square regions in terms of r?

A. \(\pi*r^2\)
B. \(\pi*r^2 + 10\)
C. \(\pi*r^2 + \frac{1}{4}*\pi^2*r^2\)
D. \(\pi*r^2 + (40 - 2\pi*r)^2\)
E. \(\pi*r^2 + (10 - \frac{1}{2}\pi*r)^2\)

The area of a circle will be - \(\pi{r^2}\) and \(2\pi{r}\) meters of wire will be used;
There will be \(40-2\pi{r}\) meters of wire left for a square. Side of this square will be \(\frac{40-2\pi{r}}{4}=10-\frac{\pi{r}}{2}\), hence the area of the square will be \((10-\frac{\pi{r}}{2})^2\).

The total area will be - \(\pi{r^2}+(10-\frac{\pi{r}}{2})^2\).

Answer: E.

OPEN DISCUSSION OF THIS QUESTION IS HERE: https://gmatclub.com/forum/a-thin-piece ... 06671.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

Re: A thin piece of wire 40 meters long is cut into two pieces. One piece &nbs [#permalink] 22 Dec 2017, 00:09
Display posts from previous: Sort by

A thin piece of wire 40 meters long is cut into two pieces. One piece

  post reply Question banks Downloads My Bookmarks Reviews Important topics  

Events & Promotions

PREV
NEXT


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®.