Find all School-related info fast with the new School-Specific MBA Forum
Learn more about the recent changes... close

It is currently 19 Jun 2013, 04:06
Customize  |  Hide

Search
Register
New posts
Unanswered

A certain IT department of fewer than 15 people hires coders

  Question banks Downloads My Bookmarks Reviews  
  Oldest Best Reply
Search for:
 
Print view
First unread post
Author Message
TAGS:
Intern
Intern
Joined: 06 Jun 2012
Posts: 31
Followers: 1

Kudos [?]: 2 [0], given: 62

A certain IT department of fewer than 15 people hires coders [#permalink] New post 12 Aug 2012, 17:46
00:00

Question Stats:

39% (02:29) correct 60% (01:47) wrong based on 43 sessions
A certain IT department of fewer than 15 people hires coders and systems administrators. Coders are paid $55,000 per year on average, while system administrators are paid an average yearly salary of $45,000. What is the ratio of coders to systems administrators?

(1) If two of the coders were made systems administrators instead, the yearly payroll for the IT department would be $535,000.

(2) If systems administrators' salaries were reduced by one-third, and coders' salaries were increased to $58,000, the department would save $57,000 in yearly payroll.
[Reveal] Spoiler: OA
2 KUDOS received
Director
Director
User avatar
Joined: 22 Mar 2011
Posts: 608
WE: Science (Education)
Followers: 46

Kudos [?]: 278 [2] , given: 43

GMAT Tests User
Re: A certain IT department of fewer than 15 people [#permalink] New post 13 Aug 2012, 01:29
2
This post received
KUDOS
Alterego wrote:
A certain IT department of fewer than 15 people hires coders and systems administrators. Coders are paid $55,000 per year on average, while system administrators are paid an average yearly salary of $45,000. What is the ratio of coders to systems administrators?

(1) If two of the coders were made systems administrators instead, the yearly payroll for the IT department would be $535,000.

(2) If systems administrators' salaries were reduced by one-third, and coders' salaries were increased to $58,000, the department would save $57,000 in yearly payroll.


Let's drop the thousands and work with smaller numbers.
Denote by A the number of administrators and by C that of the coders.

(1) We can write the following equation:
55(C - 2) + 45(A + 2) = 535, which can be written as 11C + 9A = 111.
We have to keep in mind that A + C < 15 and that A and C are positive integers.
Checking for possibile solutions under the given constraints, we find a single pair A=5 and C=6.
Sufficient.

(2) Now we can write 55C + 45A - (58C+30A) = 57.
We have to solve the equation 5A-C=19. Again, A and C must be positive integers and A + C < 15.
We find a single pair of admissible solution, A = 5 and C = 6, only if we assume that there is more than one coder.
Otherwise, we could also have the solution A = 4 and C = 1. As the question talks about administrators and coders, it is reasonable to assume that there is more than one of each type.
Sufficient.

Answer D
_________________

PhD in Applied Mathematics
Love GMAT Quant questions and running.

Intern
Intern
Joined: 04 Apr 2013
Posts: 37
Followers: 0

Kudos [?]: 4 [0], given: 13

Re: A certain IT department of fewer than 15 people [#permalink] New post 02 Jun 2013, 14:03
EvaJager wrote:
Alterego wrote:
A certain IT department of fewer than 15 people hires coders and systems administrators. Coders are paid $55,000 per year on average, while system administrators are paid an average yearly salary of $45,000. What is the ratio of coders to systems administrators?

(1) If two of the coders were made systems administrators instead, the yearly payroll for the IT department would be $535,000.

(2) If systems administrators' salaries were reduced by one-third, and coders' salaries were increased to $58,000, the department would save $57,000 in yearly payroll.


Let's drop the thousands and work with smaller numbers.
Denote by A the number of administrators and by C that of the coders.

(1) We can write the following equation:
55(C - 2) + 45(A + 2) = 535, which can be written as 11C + 9A = 111.
We have to keep in mind that A + C < 15 and that A and C are positive integers.
Checking for possibile solutions under the given constraints, we find a single pair A=5 and C=6.
Sufficient.

(2) Now we can write 55C + 45A - (58C+30A) = 57.
We have to solve the equation 5A-C=19. Again, A and C must be positive integers and A + C < 15.
We find a single pair of admissible solution, A = 5 and C = 6, only if we assume that there is more than one coder.
Otherwise, we could also have the solution A = 4 and C = 1. As the question talks about administrators and coders, it is reasonable to assume that there is more than one of each type.
Sufficient.

Answer D


why is it reasonable to assume there is more than 1 coder?
GMAT Club team member
User avatar
Joined: 02 Sep 2009
Posts: 12104
Followers: 1879

Kudos [?]: 10117 [0], given: 961

GMAT Tests User CAT Tests
Top Member of the Month
Re: A certain IT department of fewer than 15 people [#permalink] New post 02 Jun 2013, 21:21
maaadhu wrote:
EvaJager wrote:
Alterego wrote:
A certain IT department of fewer than 15 people hires coders and systems administrators. Coders are paid $55,000 per year on average, while system administrators are paid an average yearly salary of $45,000. What is the ratio of coders to systems administrators?

(1) If two of the coders were made systems administrators instead, the yearly payroll for the IT department would be $535,000.

(2) If systems administrators' salaries were reduced by one-third, and coders' salaries were increased to $58,000, the department would save $57,000 in yearly payroll.


Let's drop the thousands and work with smaller numbers.
Denote by A the number of administrators and by C that of the coders.

(1) We can write the following equation:
55(C - 2) + 45(A + 2) = 535, which can be written as 11C + 9A = 111.
We have to keep in mind that A + C < 15 and that A and C are positive integers.
Checking for possibile solutions under the given constraints, we find a single pair A=5 and C=6.
Sufficient.

(2) Now we can write 55C + 45A - (58C+30A) = 57.
We have to solve the equation 5A-C=19. Again, A and C must be positive integers and A + C < 15.
We find a single pair of admissible solution, A = 5 and C = 6, only if we assume that there is more than one coder.
Otherwise, we could also have the solution A = 4 and C = 1. As the question talks about administrators and coders, it is reasonable to assume that there is more than one of each type.
Sufficient.

Answer D


why is it reasonable to assume there is more than 1 coder?


(2) uses plural wording: "... coders' salaries were ..." so we can assume that there is more than 1 coder. Though I agree that GMAT would probably made this clearer.

Hope it's clear.
_________________

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders

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. NEW!!! ,11 Mixed Questions NEW!!!, 12 Fresh Meat NEW!!!

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. NEW!!!, 11 New DS set. NEW!!!


What are GMAT Club Tests?
25 extra-hard Quant Tests

Find out what's new at GMAT Club - latest features and updates

Intern
Intern
Joined: 04 Apr 2013
Posts: 37
Followers: 0

Kudos [?]: 4 [0], given: 13

Re: A certain IT department of fewer than 15 people [#permalink] New post 03 Jun 2013, 17:27
why is it reasonable to assume there is more than 1 coder?[/quote]

(2) uses plural wording: "... coders' salaries were ..." so we can assume that there is more than 1 coder. Though I agree that GMAT would probably made this clearer.

Hope it's clear.[/quote]

Thank You Bunuel for clarification.
Senior Manager
Senior Manager
Joined: 21 Jan 2010
Posts: 288
Followers: 0

Kudos [?]: 29 [0], given: 11

GMAT Tests User
Re: A certain IT department of fewer than 15 people hires coders [#permalink] New post 03 Jun 2013, 18:51
Alterego wrote:
A certain IT department of fewer than 15 people hires coders and systems administrators. Coders are paid $55,000 per year on average, while system administrators are paid an average yearly salary of $45,000. What is the ratio of coders to systems administrators?

(1) If two of the coders were made systems administrators instead, the yearly payroll for the IT department would be $535,000.

(2) If systems administrators' salaries were reduced by one-third, and coders' salaries were increased to $58,000, the department would save $57,000 in yearly payroll.


Just think about the problem before lifting the pen.

Department has coders(x) + system admins(y).

A) 55x + 45y = 550,000

11x + 9y = 110,000
After that use brute force to determine the value of x and y. Remember x + y <15.
You will get a unique soln.

b) 55000x+45000y-(30000y + 58000x) = 57000

Use brute force to get the answer. It will be unique.
Re: A certain IT department of fewer than 15 people hires coders   [#permalink] 03 Jun 2013, 18:51
    Similar topics Author Replies Last post
Similar
Topics:
 New posts 1 A certain class consists of fewer than 35 students. If at a andrehaui 2 15 Jul 2007, 20:26
New posts At a certain hospital, 75% of the interns receive fewer than empty_spaces 2 25 Aug 2007, 22:01
New posts 1 A certain IT dept. of fewer than 15 people hires coders and tejal777 6 17 Jul 2009, 18:23
New posts With a salary of less than 15 thousand dollars and fewer Gavan 3 24 Nov 2011, 16:57
New posts 1 The average salary of 15 people in the shipping department megafan 1 24 Dec 2012, 17:07
Display posts from previous: Sort by

A certain IT department of fewer than 15 people hires coders

  Question banks Downloads My Bookmarks Reviews  
Print view
First unread post

Moderators: VeritasPrepKarishma, Bunuel, IanStewart

Search for:


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®.

Main navigation

GMAT Resources

Partners

MBA Resources

www.gmac.com|www.mba.com