Employee X's annual salary is $12,000 more than half of Employee Y's

Question

Employee X's annual salary is $12,000 more than half of Employee Y's annual salary. Employee Z's annual salary is $15,000 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?

A. Y, Z, X
B. Y, X, Z
C. Z, X, Y
D. X, Y, Z
E. X, Z, Y

PS17680.02

A. Y, Z, X
B. Y, X, Z
C. Z, X, Y
D. X, Y, Z
E. X, Z, Y

PS17680.02

ScottTargetTestPrep · Accepted Answer

We can create the equations:

X = 12,000 + Y/2

and

Z = 15,000 + X/2

and

X = 27,500

So, we have:

27,500 = 12,000 + Y/2

15,500 = Y/2

31,000 = Y

We also, have:

Z = 15,000 + 27,500/2

Z = 15,000 + 13,750 = 28,750

Thus, X < Z < Y.

Answer: E

BradyMVP · Answer

X=$27,500

X is $12,000 more than half of Y. $27,500(X)-$12,000=$15,500. Twice of $15,500 is $31,000.
 Y is $31,000 (31,000/2=15,500. 15,500+12,000=27,500)

Z is $15,000 more than half of X.

X=$27,500. 27,500/2= 13,750. 13,750(2)=28,500

Z= $28,500

X=$27,000
Z= $27,500
Y=$31,000

X < Z < Y

Approximately 80 seconds. Roughly level 650 question imo

Posted from my mobile device

lacktutor · Answer

X= 12000 +\frac{Y}{2} 
 Z= 15000+ \frac{X}{2} 
 X= 27500

--->  Y = 15500*2= 31000 
-->  Z =15000+ 13750= 28750

X, Z, Y

Answer (E).

Archit3110 · Answer

BradyMVP 
please check highlighted part it z should be 28750 $

Ravixxx · Answer

FAST SOLUTION 
 Pick small values since you don't have to find any numbers but only their orders.

x=y+12 
 z= 15 + \frac{1}{2}x  
 x= 27

Y=27-12 =15 
 Z= 15+  \frac{1}{2} *27 
 X= 27

order: 
X, Z, Y

Answer E

100mitra · Answer

Correct option E

1. Employee X's annual salary is $12,000 more than half of Employee Y's annual salary >X = 12000 + (y/2)
2. Employee Z's annual salary is $15,000 more than half of Employee X's annual salary > Z = (x/2) +15000
3. If Employee X's annual salary is $27,500,

which of the following lists these three people in order of increasing annual salary

if X salary is 27500, X = 12000 + (y/2) = then Y = (27500-12000) *2 = 31000
If X salary is 27500, Z = (x/2) +15000 = then Z = (27500/2)+15000 = 28750
X = 27500 < Z = 28750<Y = 31000
X<Z<Y

egmat · Answer

GIVEN:   
• Employee X’s annual salary is $12000 more than half of Employee Y’s annual salary.
• Employee Z’s annual salary is $15000 more than half of Employee X’s annual salary.
• Employee X’s annual salary is $27500.

TRANSLATE THE GIVEN - Creating Equations:   
Let’s denote the annual salary of employees X, Y and Z by $x, $y, and $z, respectively. 
Then, from the three points of given information above, we can form the following three equations:
• x = 12000 + (y/2) ---- (1)
• z = 15000 + (x/2) ---- (2)
•  x = 27500 ---- (3)

GOAL:   
• To list these three people in order of increasing annual salary.

WORKING OUT:   
We will solve the system of three equations we formed above to get the values of x, y, and z. Then, comparing the three values will be a no-brainer. Let’s go!

Finding y:  
Substituting value of x from (3) into (1),
• 27500 = 12000 + (y/2)
• 15500 = (y/2)
•  y = 31000 ---- (4)

Finding z:  
Similarly, substituting value of x from (3) into (2),
• z = 15000 + (27500/2)
• z = 15000 + 13750
•  z = 28750 ---- (5)

Final answer:   
From (3), (4), and (5), we can conclude that  X < Z < Y  is the correct representation of these three people in order of increasing annual salary

Correct choice: E

Hope this helps!

Best Regards,
Ashish Arora
Quant Expert, e-GMAT

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Employee X's annual salary is $12,000 more than half of Employee Y's

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