GMAT Changed on April 16th - Read about the latest changes here

It is currently 24 Apr 2018, 01:36

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

A game at the state fair has a circular target with a radius

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

Hide Tags

3 KUDOS received
Intern
Intern
avatar
Joined: 10 Apr 2014
Posts: 5
Location: United States
GMAT 1: 630 Q39 V36
GMAT 2: 720 Q49 V40
GPA: 3.4
WE: Consulting (Consulting)
GMAT ToolKit User
A game at the state fair has a circular target with a radius [#permalink]

Show Tags

New post 25 May 2014, 22:21
3
This post received
KUDOS
10
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  85% (hard)

Question Stats:

58% (02:12) correct 42% (02:23) wrong based on 274 sessions

HideShow timer Statistics

A game at the state fair has a circular target with a radius of 10 cm on a square board measuring 30 cm on a side. Players win prizes if they throw two darts and hit only the circular area on at least one of the two attempts. What is the probability that Jim won the game?

a) 1-((9-π)/9)
b) 1-((18π-π^2)/81)
c) (9-π)/9
d) ((9-π)^2)81
e) (18π-π^2)/81
[Reveal] Spoiler: OA
Expert Post
7 KUDOS received
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 44648
Re: A game at the state fair has a circular target with a radius [#permalink]

Show Tags

New post 26 May 2014, 03:23
7
This post received
KUDOS
Expert's post
6
This post was
BOOKMARKED
brunopanta wrote:
A game at the state fair has a circular target with a radius of 10 cm on a square board measuring 30 cm on a side. Players win prizes if they throw two darts and hit only the circular area on at least one of the two attempts. What is the probability that Jim won the game?

a) 1-((9-π)/9)
b) 1-((18π-π^2)/81)
c) (9-π)/9
d) ((9-π)^2)81
e) (18π-π^2)/81


The area of the circle is \(\pi{r^2}=100\pi\);
The area of the square is \(side^2=900\).

The probability of hitting the circle is therefore \(\frac{100\pi}{900}=\frac{\pi}{9}\) and the probability of missing the circle is \(1-\frac{\pi}{9}=\frac{9-\pi}{9}\).

The probability of hitting the circle on at least one of the two attempts = 1 - {the probability of missing on both of the two attempts} =

\(1-\frac{9-\pi}{9}*\frac{9-\pi}{9}=\frac{81-(9-\pi)^2}{81}=\frac{81-(81-18\pi+{\pi}^2)}{81}=\frac{18\pi-{\pi}^2}{81}\).

Answer: E.

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

2 KUDOS received
Retired Moderator
avatar
Joined: 29 Apr 2015
Posts: 874
Location: Switzerland
Concentration: Economics, Finance
Schools: LBS MIF '19
WE: Asset Management (Investment Banking)
GMAT ToolKit User Premium Member
A game at the state fair has a circular target with a radius of 10 cm [#permalink]

Show Tags

New post 30 Jul 2015, 12:49
2
This post received
KUDOS
A game at the state fair has a circular target with a radius of 10 cm on a square board measuring 30 cm on a side. Players win prizes if they throw two darts and hit only the circular area on at least one of the two attempts. What is the probability that Jim won the game?

A. 1 - \(\frac{9-\pi}{9}\)
B. 1- \(\frac{18\pi-\pi^2}{81}\)
C. 9-\(\frac{\pi}{9}\)
D. \(\frac{(9-\pi)^2}{81}\)
E. \(\frac{18\pi-\pi^2}{81}\)
_________________

Saving was yesterday, heat up the gmatclub.forum's sentiment by spending KUDOS!

PS Please send me PM if I do not respond to your question within 24 hours.

1 KUDOS received
Senior Manager
Senior Manager
avatar
Joined: 15 Sep 2011
Posts: 347
Location: United States
WE: Corporate Finance (Manufacturing)
GMAT ToolKit User
A game at the state fair has a circular target with a radius of 10 cm [#permalink]

Show Tags

New post 30 Jul 2015, 13:50
1
This post received
KUDOS
reto wrote:
A game at the state fair has a circular target with a radius of 10 cm on a square board measuring 30 cm on a side. Players win prizes if they throw two darts and hit only the circular area on at least one of the two attempts. What is the probability that Jim won the game?

A. 1 - \(\frac{9-\pi}{9}\)
B. 1- \(\frac{18\pi-\pi^2}{81}\)
C. 9-\(\frac{\pi}{9}\)
D. \(\frac{(9-\pi)^2}{81)}\)
E. \(\frac{18\pi-\pi^2}{81}\)


Fun question. Too bad I missed it on the first attempt.
To solve:
p(success) = 1 - p(failure), where p(failure) = 1 - (Area of Target/Area of Square)
p(success) = \(1 - (1-\frac{10^{2}\pi}{30^{2}})^{2}\).
\(1-(1-\frac{\pi}{9})^{2}\)
\(1-(\frac{9-\pi}{9})^{2}\)
\(1-(\frac{81-18\pi+\pi^{2}}{81})\)
\(\frac{81-81+18\pi-\pi^{2}}{81}\)
\(\frac{18\pi-\pi^{2}}{81}\)

Answer E
Senior Manager
Senior Manager
User avatar
B
Joined: 28 Jun 2015
Posts: 297
Concentration: Finance
GPA: 3.5
Re: A game at the state fair has a circular target with a radius [#permalink]

Show Tags

New post 31 Jul 2015, 07:40
Probability of Jim hitting the circular area at least once = 1 - (not hitting the circular area).

Area of the circular target = 100 (pi).

Area of the square board = 30*30 = 900 cm^2.

Probability of hitting the circle = 100 (pi)/900 = (pi)/9.

Probability of not hitting the circle = 1 - (pi)/9 = 9 - (pi)/9.

Probability => 1 - (9 - (pi)/9)^2 = 1 - (81 - 18(pi) + (pi)^2)/81 = 18(pi) - (pi)^2/81. Ans (E).
_________________

I used to think the brain was the most important organ. Then I thought, look what’s telling me that.

Intern
Intern
avatar
B
Joined: 15 Jun 2013
Posts: 47
Schools: Ivey '19 (I)
GMAT 1: 690 Q49 V35
GPA: 3.82
Re: A game at the state fair has a circular target with a radius [#permalink]

Show Tags

New post 28 Apr 2017, 07:33
brunopanta wrote:
A game at the state fair has a circular target with a radius of 10 cm on a square board measuring 30 cm on a side. Players win prizes if they throw two darts and hit only the circular area on at least one of the two attempts. What is the probability that Jim won the game?

a) 1-((9-π)/9)
b) 1-((18π-π^2)/81)
c) (9-π)/9
d) ((9-π)^2)81
e) (18π-π^2)/81


Does anyone else thinks that this is a poor question? - It is not stated that the player always hits at least square bord (30 cm side is pretty small). The player still can hit the wall on which the square board is hanging. Therefore to area with 1 probability is much bigger (and unknown) than 900cm2.
Manager
Manager
avatar
S
Joined: 10 Sep 2015
Posts: 52
Location: India
Concentration: Finance, Human Resources
GMAT 1: 640 Q47 V31
GPA: 4
Reviews Badge
Re: A game at the state fair has a circular target with a radius [#permalink]

Show Tags

New post 16 Dec 2017, 04:20
I see generally the average time on such questions by Bunuel is near by2 mins, but i always find myself taking around 3 or more mins
is anyone else facing the same
Re: A game at the state fair has a circular target with a radius   [#permalink] 16 Dec 2017, 04:20
Display posts from previous: Sort by

A game at the state fair has a circular target with a radius

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


cron

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®.