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]

12 Aug 2012, 17:46

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46% (02:35) correct

53% (01:28) wrong

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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]

13 Aug 2012, 01:29

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Alterego wrote:

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] 13 Aug 2012, 01:29

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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

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