Find all School-related info fast with the new School-Specific MBA Forum

It is currently 31 Jul 2015, 19:32
GMAT Club Tests

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.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

Each correctional facility in a certain state has the same

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
1 KUDOS received
Senior Manager
Senior Manager
avatar
Joined: 22 Sep 2005
Posts: 279
Followers: 1

Kudos [?]: 103 [1] , given: 1

Each correctional facility in a certain state has the same [#permalink] New post 23 Jan 2008, 13:22
1
This post received
KUDOS
00:00
A
B
C
D
E

Difficulty:

(N/A)

Question Stats:

0% (00:00) correct 0% (00:00) wrong based on 0 sessions
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

Each correctional facility in a certain state has the same number of interns, and each facility has interns of each sex. If the correctional has 22% of the female interns in the state, does it have less than 20% of the male interns?

1) The Correctional has between 18% and 22% of the state's male interns.
2) The Correctional has more female interns than does any other facility in the state.
1 KUDOS received
Director
Director
avatar
Joined: 01 Jan 2008
Posts: 629
Followers: 3

Kudos [?]: 142 [1] , given: 1

Re: DS: correctional facility [#permalink] New post 23 Jan 2008, 13:45
1
This post received
KUDOS
1 is sufficient, let's denote x - total number of female interns in the state, y - total number of male interns in the state, d - percent of the male interns in the considered facility. We know d is between 18% and 22%.

Total number of facilities is (x+y)/(22%*x+d*y) = n, it's easy to show that 4 < n < 6

(x+y)/(22%*x+d*y) <= (x+y)/(22%*x + 18%*d) < (x+y)/(18%*x+18%*y) = 1/18% < 6
(x+y)/(22%*x + d*y) >= (x+y)/(22%*x + 22%*y) = 1/22% > 4

Therefore, n = 5, then d < 20%


2 is sufficient -> there are at least 4 other facilities or 5 total (22%*4 = 88% < 100%), in each facility there are more male interns than in the considered facility. Therefore percentage of male interns in the considered facility is below 20% of the male interns in the state
Expert Post
CEO
CEO
User avatar
Joined: 17 Nov 2007
Posts: 3574
Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
GMAT 1: 750 Q50 V40
Followers: 424

Kudos [?]: 2293 [0], given: 359

GMAT ToolKit User Premium Member
Re: DS: correctional facility [#permalink] New post 23 Jan 2008, 22:12
Expert's post
Good question and answer.
+1+1
_________________

HOT! GMAT TOOLKIT 2 (iOS) / GMAT TOOLKIT (Android) - The OFFICIAL GMAT CLUB PREP APP, a must-have app especially if you aim at 700+ | PrepGame

Director
Director
User avatar
Joined: 03 Sep 2006
Posts: 884
Followers: 6

Kudos [?]: 307 [0], given: 33

GMAT ToolKit User
Re: DS: correctional facility [#permalink] New post 24 Jan 2008, 00:06
total males =M
total females =F
total interns = (M+F)
total number of correctional facilities = n
Each has no. of interns = (M+F)/n
Each has no. of females = (22/100)*F
Each has male interns = x such that => (18/100)*M < x < (22/100)*M
(M+F)/n = (22/100)*F + x

x= (M+F)/n - (22/100)*F

(18/100)*M < (M+F)/n - (22/100)*F < (22/100)*M

how do you get n = 5?

in this case each correctional facility has (M+F)/n interns, but that does not mean each has M/n and F/n interns.

M can be 100, F can be 5 and vice versa!

Could you please explain in detail?
Director
Director
avatar
Joined: 01 Jan 2008
Posts: 629
Followers: 3

Kudos [?]: 142 [0], given: 1

Re: DS: correctional facility [#permalink] New post 24 Jan 2008, 06:20
LM wrote:
Each has no. of interns = (M+F)/n
Each has no. of females = (22/100)*F
Each has male interns = x such that => (18/100)*M < x < (22/100)*M
Could you please explain in detail?


LM, it's not "each" but only one correctional facility. One particular correctional facility has 22% of female interns (22/100)*F and has d*M males -> total number of interns in the facility is (22/100)*F + d*M. Since each facility has the same total number of interns (F+M)/((22/100)*F + d*M) has to be a positive integer. Using inequalities I showed that the integer is greater than 4 and less than 6. It has to be equal to 5. Since there are more than 1/5 female interns, d < 1/5, otherwise the facility will have more than 1/5 of all interns which contradicts the condition that each facility has the same number of interns.
Senior Manager
Senior Manager
avatar
Joined: 22 Sep 2005
Posts: 279
Followers: 1

Kudos [?]: 103 [0], given: 1

Re: DS: correctional facility [#permalink] New post 24 Jan 2008, 10:39
You are right.

OA is D
Re: DS: correctional facility   [#permalink] 24 Jan 2008, 10:39
Display posts from previous: Sort by

Each correctional facility in a certain state has the same

  Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Privacy Policy| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group and phpBB SEO

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®.