It is currently 18 Jan 2018, 13:18

### 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

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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

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

Author Message
TAGS:

### Hide Tags

Intern
Joined: 10 Apr 2014
Posts: 5

Kudos [?]: 28 [3], given: 23

Location: United States
GMAT 1: 630 Q39 V36
GMAT 2: 720 Q49 V40
GPA: 3.4
WE: Consulting (Consulting)
A game at the state fair has a circular target with a radius [#permalink]

### Show Tags

25 May 2014, 21:21
3
KUDOS
9
This post was
BOOKMARKED
00:00

Difficulty:

85% (hard)

Question Stats:

58% (02:08) correct 42% (02:19) wrong based on 249 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

Kudos [?]: 28 [3], given: 23

Math Expert
Joined: 02 Sep 2009
Posts: 43323

Kudos [?]: 139430 [7], given: 12790

Re: A game at the state fair has a circular target with a radius [#permalink]

### Show Tags

26 May 2014, 02:23
7
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} =

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

Hope it's clear.
_________________

Kudos [?]: 139430 [7], given: 12790

Retired Moderator
Joined: 29 Apr 2015
Posts: 888

Kudos [?]: 1990 [2], given: 302

Location: Switzerland
Concentration: Economics, Finance
Schools: LBS MIF '19
WE: Asset Management (Investment Banking)
A game at the state fair has a circular target with a radius of 10 cm [#permalink]

### Show Tags

30 Jul 2015, 11:49
2
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.

Kudos [?]: 1990 [2], given: 302

Senior Manager
Joined: 15 Sep 2011
Posts: 358

Kudos [?]: 443 [1], given: 46

Location: United States
WE: Corporate Finance (Manufacturing)
A game at the state fair has a circular target with a radius of 10 cm [#permalink]

### Show Tags

30 Jul 2015, 12:50
1
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) = $$1 - (1-\frac{10^{2}\pi}{30^{2}})^{2}$$.
$$1-(1-\frac{\pi}{9})^{2}$$
$$1-(\frac{9-\pi}{9})^{2}$$
$$1-(\frac{81-18\pi+\pi^{2}}{81})$$
$$\frac{81-81+18\pi-\pi^{2}}{81}$$
$$\frac{18\pi-\pi^{2}}{81}$$

Kudos [?]: 443 [1], given: 46

Senior Manager
Joined: 28 Jun 2015
Posts: 299

Kudos [?]: 115 [0], given: 47

Concentration: Finance
GPA: 3.5
Re: A game at the state fair has a circular target with a radius [#permalink]

### Show Tags

31 Jul 2015, 06:40
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.

Kudos [?]: 115 [0], given: 47

Intern
Joined: 15 Jun 2013
Posts: 47

Kudos [?]: 14 [0], given: 33

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

28 Apr 2017, 06:33
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.

Kudos [?]: 14 [0], given: 33

Intern
Joined: 10 Sep 2015
Posts: 44

Kudos [?]: 19 [0], given: 64

Location: India
Concentration: Finance, Human Resources
GMAT 1: 640 Q47 V31
GPA: 4
Re: A game at the state fair has a circular target with a radius [#permalink]

### Show Tags

16 Dec 2017, 03:20
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

Kudos [?]: 19 [0], given: 64

Re: A game at the state fair has a circular target with a radius   [#permalink] 16 Dec 2017, 03:20
Display posts from previous: Sort by