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?

GMAT Panda · Accepted Answer

X, Z, Y We name variables for each employee's annual salary. X = Employee X's annual salary Y = Employee Y's annual salary Z = Employee Z's annual salary We translate the relationship for Employee X using the phrase "Employee X's annual salary is 12,000USD more than half of Employee Y's annual salary". X = 1/2Y + 12000 We substitute the known value of X into the equation and solve for Y. 27500 = 1/2Y + 12000 27500 - 12000 = 1/2Y 15500 = 1/2Y Y = 31000 We translate the relationship for Employee Z using the phrase "Employee Z's annual salary is 15,000USD more than half of Employee X's annual salary". Z = 1/2X + 15000 We substitute the known value of X into the equation and solve for Z. Z = 1/2 27500 + 15000 Z = 13750 + 15000 Z = 28750 We compare the salaries of X, Z, and Y to find the order from smallest to largest. 27500 < 28750 < 31000

Explanation	Calculations	Help
$We name variables for each employee's annual salary.$	$X = Employee X’s annual salary Y = Employee Y’s annual salary Z = Employee Z’s annual salary$
$We translate the relationship for Employee X using the phrase "Employee X’s annual salary is 12,000USD more than half of Employee Y’s annual salary" .$	$X = \frac{1}{2} Y + 12000$
$We substitute the known value of X into the equation and solve for Y.$	$27500 = \frac{1}{2} Y + 12000 27500 - 12000 = \frac{1}{2} Y 15500 = \frac{1}{2} Y Y = 31000$
$We translate the relationship for Employee Z using the phrase "Employee Z’s annual salary is 15,000USD more than half of Employee X’s annual salary" .$	$Z = \frac{1}{2} X + 15000$
$We substitute the known value of X into the equation and solve for Z.$	$Z = \frac{1}{2} \times 27500 + 15000 Z = 13750 + 15000 Z = 28750$
$We compare the salaries of X, Z, and Y to find the order from smallest to largest.$	$27500 < 28750 < 31000$

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