GMAT Practice Question: Employee X's annual salary is 12,000USD more than half of Employee Y's annual salary. Employee...
Question
Employee X's annual salary is 12,000USD more than half of Employee Y's annual salary. Employee Z's annual salary is 15,000USD more than half of Employee X's annual salary. If Employee X's annual salary is 27,500, which of the following lists these three people in order of increasing annual salary?
- Y, Z, X
- Y, X, Z
- Z, X, Y
- X, Y, Z
- X, Z, Y
Topics: word problems, linear equations, order, translations
Solution
Step 1
We name variables for each employee's annual salary.
X = \text{Employee X's annual salary} Y = \text{Employee Y's annual salary} Z = \text{Employee Z's annual salary}
Step 2
We translate the relationship for Employee X using the phrase \textbf{\text{"Employee X's annual salary is 12,000USD more than half of Employee Y's annual salary"}}.
X = \frac{1}{2}Y + 12000
Step 3
We substitute the known value of X into the equation and solve for Y.
27500 = \frac{1}{2}Y + 12000 27500 - 12000 = \frac{1}{2}Y 15500 = \frac{1}{2}Y Y = 31000
Step 4
We translate the relationship for Employee Z using the phrase \textbf{\text{"Employee Z's annual salary is 15,000USD more than half of Employee X's annual salary"}}.
Z = \frac{1}{2}X + 15000
Step 5
We substitute the known value of X into the equation and solve for Z.
Z = \frac{1}{2}\times 27500 + 15000 Z = 13750 + 15000 Z = 28750
Step 6
We compare the salaries of X, Z, and Y to find the order from smallest to largest.
27500 < 28750 < 31000
Answer
X, Z, Y
