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

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

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12 Aug 2012, 17:46
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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. Director Joined: 22 Mar 2011 Posts: 604 WE: Science (Education) Re: A certain IT department of fewer than 15 people [#permalink] ### Show Tags 13 Aug 2012, 01:29 3 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
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Re: A certain IT department of fewer than 15 people  [#permalink]

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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? _________________ Maadhu MGMAT1 - 540 ( Trying to improve ) Math Expert Joined: 02 Sep 2009 Posts: 47200 Re: A certain IT department of fewer than 15 people [#permalink] ### Show Tags 02 Jun 2013, 21:21 1 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.
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Re: A certain IT department of fewer than 15 people  [#permalink]

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

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03 Jun 2013, 18:51
1
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. Intern Joined: 05 Jun 2014 Posts: 6 Location: India GMAT 1: 610 Q44 V34 WE: Engineering (Computer Software) Re: A certain IT department of fewer than 15 people hires coders [#permalink] ### Show Tags 31 Jan 2015, 08:37 In this case it is coders + sys administrators < 11.. How is it possible to test a wide range of values ? At least if it was c + s = 11 we would have limited options, but since the situation here is c + s <11, there can be do many options Manager Joined: 22 Jan 2014 Posts: 168 WE: Project Management (Computer Hardware) 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)

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

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31 Jan 2015, 13:09
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.

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Special Offer: Save $75 + GMAT Club Tests Free Official GMAT Exam Packs + 70 Pt. Improvement Guarantee www.empowergmat.com/ ***********************Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!*********************** Current Student Joined: 06 Mar 2014 Posts: 256 Location: India GMAT Date: 04-30-2015 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.
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Re: A certain IT department of fewer than 15 people hires coders  [#permalink]

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07 Apr 2015, 21:55
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. _________________ Karishma Private Tutor for GMAT Contact: bansal.karishma@gmail.com Manager Joined: 01 Mar 2014 Posts: 129 Schools: Tepper '18 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?
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Re: A certain IT department of fewer than 15 people hires coders  [#permalink]

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22 May 2016, 21:45
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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?

Case 2 in this post discusses this concept: http://www.veritasprep.com/blog/2011/06 ... -of-thumb/

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

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