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.
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