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?

1. Y, Z, X
2. Y, X, Z
3. Z, X, Y
4. X, Y, Z
5. X, Z, Y

“Employee X's annual salary is $12,000 more than half of Employee Y’s''- is a topic of the GMAT Quantitative reasoning section of the GMAT exam. GMAT quant section analyses the numerical proficiency of the candidates to solve mathematical problems. The students must calculate the question properly with accurate quantitative logic. The students must gather sufficient ideas about mathematical calculations to crack GMAT Problem Solving questions. The GMAT Quant topic in the problem-solving part mentions mathematical problems that must be solved with appropriate quantitative aptitudes. The candidates can practice questions by answering from the book “GMAT Official Guide Quantitative Review 2022”.

Solution and Explanation:

Approach Solution 1:

The problem statement informs that:

Given:

• Employee X's annual salary is $12,000 more than ½ of Employee Y's annual salary.
• Employee Z's annual salary is $15,000 more than ½ of Employee X's annual salary.
• Employee X's annual salary is $27,500

Asked:

• To arrange the annual salary of these three people in increasing order.

Since X's salary is $12,000 more than ½ of Employee Y's salary, then we can say,
X = 12,000 + Y/2

Since Z's salary is $15,000 more than ½ of Employee X's salary, then we get,
Z = 15,000 + X/2

As per the question, X = 27,500
Therefore, by putting the value of X in the equation X = 12,000 + Y/2, we get:
=>27,500 = 12,000 + Y/2
=>15,500 = Y/2
=>31,000 = Y

Similarly, by putting the value of X in the equation Z = 15,000 + X/2, we get,
=>Z = 15,000 + 27,500/2
=>Z = 15,000 + 13,750 = 28,750

Thus, we can say X < Z < Y.

Correct Answer: (E)

Approach Solution 2:

The problem statement suggests that:

Given:

• Employee X's annual salary is $12,000 more than ½ of Employee Y's annual salary.
• Employee Z's annual salary is $15,000 more than ½ of Employee X's annual salary.
• Employee X's annual salary is $27,500

Asked:

• To arrange the annual salary of these three people in increasing order.

As per the question, the value of X = $27,500
Since X’s salary is $12,000 more than half of Y’s salary.

Therefore, half of Y’s salary = $27,500(X) - $12,000 = $15,500.
Therefore, the salary of Y= 2* $15,500 = $31,000.

Since Z’s salary is $15,000 more than half of X’s salary and X=$27,500.
Therefore, we get, Z= $15,000 +$ 27,500/2 =$ 28,750

X=$27,500
Z= $28,750
Y=$31,000

Thus, the arrangement will be X < Z < Y.

Correct Answer: (E)

Approach Solution 3:

The problem statement states that:

Given:

• Employee X's annual salary is $12,000 more than ½ of Employee Y's annual salary.
• Employee Z's annual salary is $15,000 more than ½ of Employee X's annual salary.
• Employee X's annual salary is $27,500

Asked:

• To arrange the annual salary of these three people in increasing order.

We can solve the sum by using this fastest method. To do this, we need to take small values.

As per the conditions of the questions:
X =y/2 + 12
Z =x/2 + 15
X =27

Therefore, by simplifying the equations, we get,
Y = (27- 12)*2 = 30
Z = 27/2 + 15
X = 27

Hence, the arrangement will be X < Z < Y.

Correct Answer: (E)

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