An analysis of the monthly incentives received by 5 salesmen : The mean and median of the incentives is $7000. The only mode among the observations is $12,000. Incentives paid to each salesman were in full thousands. What is the difference V between the highest and the lowest incentive received by the 5 salesmen in the month?
Choose the most appropriate option:
A) $4000
B) $5000
C) $9000
D) $11,000
E) $13,000
Break down the question in to steps:   Step #1: incentives received by 5 salesmen --&gt;abcde   Step #2: mean and median of the incentives is $7000: via number properties --&gt; total incentives = 7,000 * 5 = 35, 000ab7,000de   Step #3: only mode among the observations is $12,000: mode is the value that appears most often in a set of data. Therefore 12,000 must occur more then once and since 12,000 is larger than the mean (7,000) the most it can occur is twice in our list. If we place the numbers in ascending order we haveab7,00012,00012,000   Step #4: What is the difference between the highest and the lowest incentive:   - The total paid has to equal mean * # of numbers = 7,000 * 5 = 35 000.   - The three values we have so far (12,000 12,000 and 7, 000) equal 31,000.   - Therefore the first two numbers( ab) must equal 4, 000   - There is only one mode which is 12,000, therefore 4,000 must be equal to a set of two numbers that are not the and a &lt; b   if a = 1,000 b = 3,000 --&gt; difference V between the highest and the lowest incentive = 12,000 - 1,000 =11, 000   no other options for a or b to fit the criteria   Final List:1,0003,0007,00012,00012,000   Answer $11,000
<result>D</result>
An analysis of the monthly incentives received by 5 salesmen : The mean and median of the incentives is $7000. The only mode among the observations is $12,000. Incentives paid to each salesman were in full thousands. What is the difference V between the highest and the lowest incentive received by the 5 salesmen in the month?