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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.

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

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13 Aug 2012, 01:29

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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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PhD in Applied Mathematics Love GMAT Quant questions and running.

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?
_________________

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]

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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.
_________________

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

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03 Jun 2013, 18:51

1

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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]

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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)

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]

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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.

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]

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19 May 2016, 11:11

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

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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?

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.
_________________

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