Data Sufficiency

A certain lT department of fewer than '15 people
hires coders and systems administrators. Coders
are paid $55,000 per year on average, while
systems administrators are paid an average yearly
salary of $45,000. What is the ratio of coders to
systems administrators?
(1) lf two of the coders were made systems
administrators instead, the yearly payroll
for the lT department would be $535,000.
(2 lf 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.

rakaisraka wrote:A certain lT department of fewer than '15 people
hires coders and systems administrators. Coders
are paid $55,000 per year on average, while
systems administrators are paid an average yearly
salary of $45,000. What is the ratio of coders to
systems administrators?
(1) lf two of the coders were made systems
administrators instead, the yearly payroll
for the lT department would be $535,000.
(2 lf 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 c = coders and s = system administrators.

Statement 1:
55,000(c-2) + 45,000(s+2) = 535,000
55(c-2) + 45(s+2) = 535
11(c-2) + 9(s+2) = 107.

Implication of the resulting equation:
(multiple of 11) + (multiple of 9) = 107
(multiple of 9) = 107 - (multiple of 11).

Subtract multiples of 11 from 107.
The result must be a multiple of 9.
107-99=8.
107-88=19.
107-77=30.
107-66=41.
107-55=52.
107-44=63.
107-33=74.
107-22=85.
107-11=96.

Only the option in red yields a multiple of 9.
In this option, 11(c-2) = 44 and 9(s+2)=63, implying that c=6 and s=5.
Thus, c/s = 6/5.
SUFFICIENT.

Statement 2:
System administrator salaries reduced by 1/3 = (2/3)(45,000s) = 30,000s.
Coder salaries increased to 58,000 = 58,000c.
Total of new salaries = 58,000c + 30,000s.
Old total = 55,000c + 45,000s.

Since the new total is 57,000 less than the old total, we get:
55,000c + 45,000s - 57000 = 58,000c + 30,000s
55c + 45s - 57 = 58c + 30s
15s - 3c = 57
5s - c = 19
5s = c+19
s = (c+19)/5.

Case 1: c=1, s=4
In this case, c/s = 1/4.
Case 2: c=6, s=5
In this case, c/s = 6/5.
Since different ratios are possible, INSUFFICIENT.

The correct answer is A.

Please note the following:
Some sources incorrectly cite D as the OA.
As shown in my solution above, the OA is in fact A.

Hi Mitch, I got confused here.. It says IT company with less than 15 Employees hires coders and system admins. DOes it NOT mean that there are coders , system admins and other employees? Because of this i was not able to make the equation.

Thanks

rakaisraka wrote:Hi Mitch, I got confused here.. It says IT company with less than 15 Employees hires coders and system admins. DOes it NOT mean that there are coders , system admins and other employees? Because of this i was not able to make the equation.

Thanks

Your concern is understandable.
The GMAT would make it clear that every employee in the IT department is either a coder or a system administrator.
A better wording might be as follows:
A certain lT department has fewer than 15 employees. Each employee is either a coder or a system administrator.

Hi Mitch,
Took >3 min to solve.Is there any easier/less time consuming approach?