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Wed Mar 04, 2020 2:44 am

Princeton Review

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 administrator 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.

OA D

Say the department hires x no. of coders and y no. of admins. Thus, x + y < 15.

We have to get the value of x/y.

Let's take each statement one by one.

1) If two of the coders were made systems administrator instead, the yearly payroll for the IT department would be $535,000.

Since the salary of a coder ($55k) is $10k greater than that of an admin, the yearly payroll of the department would be $535k + 2*10 = $555k

Thus, we have 55kx + 45ky = 555k

=> 11x + 9y = 111

y = (111 – 11x)/9
y = 12 + (3 – 11x)/9

Since x and y are positive integers, the first qualifying value of x would be 6 and that of y would be 5. Since x + y = 11 < 15, these are acceptable values. There may be many more qualifying values of x and y, but they would not be acceptable as for those values, x + y would be greater than 15.

Thus, x/y = 6/5. Sufficient.

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.

Revised salary of an admin = 2/3 of 45k = 30k;
Revised salary of a coder = 58k

=> (55x + 45y) – (58x + 30y) = 57k

5y – x = 19

y = (19 + x)/5
y = 3 + (4 + x)/5

@x = 1, y = 4; however, since the question uses the plural for coders, we can assume that x > 1; similarly, y > 1.

@x = 6, y = 5. Thus, x/y = 6/5. Sufficient.

The correct answer: D

Hope this helps!

-Jay
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