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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] New post 12 Aug 2012, 16:46
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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.
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Re: A certain IT department of fewer than 15 people [#permalink] New post 13 Aug 2012, 00:29
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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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Re: A certain IT department of fewer than 15 people [#permalink] New post 02 Jun 2013, 13:03
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?
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Re: A certain IT department of fewer than 15 people [#permalink] New post 02 Jun 2013, 20:21
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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] New post 03 Jun 2013, 16:27
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] New post 03 Jun 2013, 17:51
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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] 03 Jun 2013, 17:51
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