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# An analysis of the monthly incentives received by 5 salesmen : The mea

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An analysis of the monthly incentives received by 5 salesmen : The mea  [#permalink]

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14 Feb 2016, 04:45
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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 between the highest and the lowest incentive received by the 5 salesmen in the month?

A. \$4000
B. \$5000
C. \$9000
D. \$11,000
E. \$13,000

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An analysis of the monthly incentives received by 5 salesmen : The mea  [#permalink]

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14 Feb 2016, 09:37
Bunuel wrote:
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 between the highest and the lowest incentive received by the 5 salesmen in the month?

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 --> a b c d e

Step #2: mean and median of the incentives is \$7000: via number properties --> total incentives = 7,000 * 5 = 35, 000 & a b 7,000 d e

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 have a b 7,000 12,000 12,000

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( a & b) 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 < b
if a = 1,000 b = 3,000 --> difference 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: 1,000 3,000 7,000 12,000 12,000
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Re: An analysis of the monthly incentives received by 5 salesmen : The mea  [#permalink]

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04 Jan 2018, 15:34
Hi All,

This prompt gives us several Facts to work with:
1) There are 5 values
2) Both the MEAN and the MEDIAN = \$7,000
3) There's only one MODE and it's \$12,000
4) Each value is a multiple of \$1,000

We're asked for the difference between the greatest and least of the five values.....

Since the MEAN = \$5,000, we know that the TOTAL of the 5 values is... (5)(\$7,000) = \$35,000

With a MEDIAN of \$7,000, we know that two values are GREATER than \$7,000 (and they're BOTH the MODE: \$12,000 each) and two are LESS than \$7,000.

_ _ \$7,000 \$12,000 \$12,000 = two unknowns + \$31,000 = \$35,000
two unknowns = \$4,000

The two unknowns must be DIFFERENT from one another (because there was just the one MODE) and both must be multiples of \$1,000... thus, they must be \$1,000 and \$3,000. The difference between the greatest and least values is \$12,000 - \$1,000 = \$11,000

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Re: An analysis of the monthly incentives received by 5 salesmen : The mea  [#permalink]

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31 Oct 2019, 17:31
Bunuel wrote:
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 between the highest and the lowest incentive received by the 5 salesmen in the month?

A. \$4000
B. \$5000
C. \$9000
D. \$11,000
E. \$13,000

From the information given in the problem, we see that the highest 3 incentives are \$7,000, \$12,000 and \$12,000, and the total amount of the 5 incentives is 5 x 7,000 = \$35,000. Therefore, the total of the lowest 2 incentives is 35,000 - (7,000 + 12,000 + 12,000) = 35,000 - 31,000 = \$4,000. Since those 2 incentives are paid in full thousands and they can’t be each \$2,000 (since there is only one mode), they are in the amounts of \$1,000 and \$3,000. So the difference between the highest and the lowest incentives is 12,000 - 1,000 = \$11,000.

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Re: An analysis of the monthly incentives received by 5 salesmen : The mea  [#permalink]

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01 Nov 2019, 10:17
Awesome question, thanks for posting!
Intern
Joined: 25 Jan 2020
Posts: 1
Re: An analysis of the monthly incentives received by 5 salesmen : The mea  [#permalink]

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27 Mar 2020, 19:05
for Mean= Median, all the entries should be symmetric. but the entries which you have written here are not symmetric. can you please explain?
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Joined: 19 Jan 2020
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Re: An analysis of the monthly incentives received by 5 salesmen : The mea  [#permalink]

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28 Mar 2020, 03:00
for Mean= Median, all the entries should be symmetric. but the entries which you have written here are not symmetric. can you please explain?
I was wondering the same. Bunuel
Re: An analysis of the monthly incentives received by 5 salesmen : The mea   [#permalink] 28 Mar 2020, 03:00