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.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

A certain IT department of fewer than 15 people hires coders [#permalink]

Show Tags

12 Aug 2012, 17:46

8

This post was BOOKMARKED

00:00

A

B

C

D

E

Difficulty:

95% (hard)

Question Stats:

44% (03:26) correct
56% (02:34) wrong based on 200 sessions

HideShow timer Statistics

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.

Re: A certain IT department of fewer than 15 people [#permalink]

Show Tags

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.

Re: A certain IT department of fewer than 15 people [#permalink]

Show Tags

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? _________________

Re: A certain IT department of fewer than 15 people [#permalink]

Show Tags

02 Jun 2013, 21:21

Expert's post

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.

Re: A certain IT department of fewer than 15 people [#permalink]

Show Tags

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. _________________

Re: A certain IT department of fewer than 15 people hires coders [#permalink]

Show Tags

03 Jun 2013, 18:51

1

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.

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]

Show Tags

31 Jan 2015, 12:00

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

Shouldn't we be multiplying the LHS by 12? (considering that the figures given are avg salaries and RHS is denoting yearly payout)

Re: A certain IT department of fewer than 15 people hires coders [#permalink]

Show Tags

31 Jan 2015, 13:09

Expert's post

Hi saleem1992,

We have two pieces of information that limit the possibilities: the number of each type of worker AND either the total salaries (in Fact 1) or the money saved (in Fact 2).

As an example of how there are limited options, consider what were told in Fact 1....

Fact 1: ......the yearly payroll for the IT department would be $535,000.

$535,000 is a rather specific number and it's made up of a certain number of $55,000 employees and $45,000 employees. While it would take a bit of 'brute force' work, it wouldn't take that much to eliminate the wrong answers.

For example: 10 Coders = 10(55k) = 550,000 which is TOO MUCH MONEY. Therefore, the number of coders MUST be less than 10. 9 Coders = 9(55k) = 495,000, leaving 40,000 left over, but that's not the right amount of money for another employee. The number of coders CANNOT = 9 either. Etc.

Working down, you'll eventually find that there's just one set of values that fits these parameters. Thus, Fact 1 is SUFFICIENT.

Re: A certain IT department of fewer than 15 people hires coders [#permalink]

Show Tags

07 Apr 2015, 16:56

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.

I have a problem with the wording of the question. Just want to confirm is it me or the fact that the opening statement says the IT Dept "Hires" coders and systems administrators makes it seem like total number = Already present IT people (less than 15) + Coders and System Admin.

That interpretation could be avoided in my view if the Question did not add "hires"

Please let me know if i am missing something in the language of the original question.

Re: A certain IT department of fewer than 15 people hires coders [#permalink]

Show Tags

07 Apr 2015, 21:55

Expert's post

earnit 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.

I have a problem with the wording of the question. Just want to confirm is it me or the fact that the opening statement says the IT Dept "Hires" coders and systems administrators makes it seem like total number = Already present IT people (less than 15) + Coders and System Admin.

That interpretation could be avoided in my view if the Question did not add "hires"

Please let me know if i am missing something in the language of the original question.

Yes, the word "hires" could have been avoided since it hints at additions to the total number i.e. 15. But the rest of the question clarifies that "hires" means the team has "coders" and "system administrators". Mind you, even in the actual GMAT, the wording will not be what we want. Overall, the question should clarify and not leave any ambiguity. This question does a reasonable job of that and is hence acceptable. _________________

Re: A certain IT department of fewer than 15 people hires coders [#permalink]

Show Tags

19 May 2016, 11:11

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email. _________________

Re: A certain IT department of fewer than 15 people hires coders [#permalink]

Show Tags

20 May 2016, 10:30

VeritasPrepKarishma wrote:

earnit 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.

I have a problem with the wording of the question. Just want to confirm is it me or the fact that the opening statement says the IT Dept "Hires" coders and systems administrators makes it seem like total number = Already present IT people (less than 15) + Coders and System Admin.

That interpretation could be avoided in my view if the Question did not add "hires"

Please let me know if i am missing something in the language of the original question.

Yes, the word "hires" could have been avoided since it hints at additions to the total number i.e. 15. But the rest of the question clarifies that "hires" means the team has "coders" and "system administrators". Mind you, even in the actual GMAT, the wording will not be what we want. Overall, the question should clarify and not leave any ambiguity. This question does a reasonable job of that and is hence acceptable.

I got to the equations but wasn't sure of how to solve these. I have come across such questions before as well where one equation with 2 variables can be solved. Is there a way of doing this? I find it extremely tough to just put in numbers. How can we be sure that there is a unique solution?

Re: A certain IT department of fewer than 15 people hires coders [#permalink]

Show Tags

22 May 2016, 21:45

Expert's post

MeghaP wrote:

I got to the equations but wasn't sure of how to solve these. I have come across such questions before as well where one equation with 2 variables can be solved. Is there a way of doing this? I find it extremely tough to just put in numbers. How can we be sure that there is a unique solution?

It shows you how to get all integer solutions given an equation in two variables. Sometimes, you will get one unique solution to the equation. The post tells you how to find it. _________________

Part 2 of the GMAT: How I tackled the GMAT and improved a disappointing score Apologies for the month gap. I went on vacation and had to finish up a...

So the last couple of weeks have seen a flurry of discussion in our MBA class Whatsapp group around Brexit, the referendum and currency exchange. Most of us believed...

This highly influential bestseller was first published over 25 years ago. I had wanted to read this book for a long time and I finally got around to it...