Each employee on a certain task force is either a manager or a

Question

Each employee on a certain task force is either a manager or a director. If the range of the salaries of the directors on the task force is $3,000 and the range of the salaries of the managers on the task force is $1,000, what is the least possible range of the salaries of all of the employees on the task force?

A. $1,000
B. $2,000
C. $3,000
D. $4,000
E. $5,000

Can all employees be managers?

Bunuel · Accepted Answer

The range is the difference between the largest and smallest values in a set. Therefore, the least possible range for the combined salaries of all employees cannot be less than the largest individual range. Since the largest individual range is $3,000 (for directors), the least possible overall range is also $3,000.

Answer: C.

gmatophobia · Answer

Minimum Salary of Director =  d_{	ext{min}}  
 Maximum Salary of Director =  d_{	ext{min}} + 3000

Minimum Salary of Manager =  m_{	ext{min}}  
 Maximum Salary of Manager =  m_{	ext{min}} + 1000

Possible Range of the salaries of all of the employees on the task force

To find the minimum range, the range of one of the groups should be within another group. As the range of the salaries of directors is greater than range of the salaries of the managers, the minimum range is 3000

Option C

Bunuel · Answer

Similar question from GMAT Prep Focus: https://gmatclub.com/forum/the-range-of ... 25057.html

Diwen2000 · Answer

Can all employees be managers?

Bunuel · Answer

No. There must be at least two managers and at least two directors. We are told that the range of the directors' salaries on the task force is $3,000. The range is the difference between the highest and lowest values in a set. Since the range is a positive value, there must be at least two directors.

IJIJ · Answer

I dont understand the answer. Why are we assuming that the manager's salary lies between the director's?

Why cant we assume that the manager's salary and the director's salary are non-overlapping sets?

Bunuel · Answer

We're not assuming the ranges overlap by default. But since the question asks for the least possible range, we place the $1,000 manager range fully within the $3,000 director range. That gives the smallest total range possible, which is $3,000.

lily123400 · Answer

I got this question wrong the first time but I see now the solution is very simple. I got tripped up over the wording. 
Since the Directors have at least a 3000$ range, there's no possible way the overall range would be less than that no matter what the manager range is. That eliminates A and B. 
Then, if we assume the Director and the Manager start at the same salary, we can see that the D+3000 is the most.
D+3000 - D = 3000

Each employee on a certain task force is either a manager or a

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

Each employee on a certain task force is either a manager or a

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards