GMAT Exam > GMAT Questions > An analysis of the monthly incentives receive...
Start Learning for Free
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)$13,000
- c)$9000
- d)$5000
- e)$11,000
Correct answer is option 'E'. Can you explain this answer?
Verified Answer
An analysis of the monthly incentives received by 5 salesmen : The mea...
Hints to solve this question:
- Mean and Median = $7000. So, find the third highest incentive.
- Only one mode; mode = $12,000.
- Use hint 1 and hint 2 to find how many executives have got $12,000.
- Now compute the sum of incentives got by those who got neither $7000 nor $12000.
Step 1: Understanding the given data
- The arithmetic mean of the incentives is $7000.
- The median of the incentives is also $7000.
- There is only one mode and the mode is $12,000.
Step 2: Decoding Mean and Median
Let their incentives be a, b, c, d, and e such that a ≤ b ≤ c ≤ d ≤ e
Therefore, the median of these values is 'c'.
The median incentive is $7000. So, c = $7000.
The median incentive is $7000. So, c = $7000.
Essentially, the incentives are __ __ 7000 __ __
The arithmetic mean of the incentives is $7000.
So, the sum of their incentives a + b + c + d + e = 5 * 7000 = $35,000
So, the sum of their incentives a + b + c + d + e = 5 * 7000 = $35,000
Step 3: Decoding Mode
There is only one mode amongst these 5 observations.
The mode is that value that appears with the maximum frequency.
Hence, $12,000 is the incentive received by the most number of salesmen.
The mode is that value that appears with the maximum frequency.
Hence, $12,000 is the incentive received by the most number of salesmen.
So, the incentives are __ __ 7000, 12000, 12000
Step 4: Putting it all together
The incentive that c has got is $7000
The incentive received by d and e are 12,000 each
The incentive received by d and e are 12,000 each
Therefore, c + d + e = 7000 + 12,000 + 12,000 = $31,000
Hence, a + b = 35,000 - 31,000 = $4000
Hence, a + b = 35,000 - 31,000 = $4000
As there is only one mode, the incentives received by a and b have to be different.
So, a received $1000 and b received $3000.
So, a received $1000 and b received $3000.
Maximum incentive: $12,000
Minimum incentive: $1000
Difference between maximum and minimum incentive: $11,000
Minimum incentive: $1000
Difference between maximum and minimum incentive: $11,000
Choice E is the correct answer.
Most Upvoted Answer
An analysis of the monthly incentives received by 5 salesmen : The mea...
Analysis of Monthly Incentives
The mean and median of the incentives is $7000, and the only mode is $12,000. This information gives us an insight into the distribution of the incentives received by the 5 salesmen.
Difference between the Highest and Lowest Incentive
To find the difference between the highest and lowest incentive received by the salesmen, we need to consider the mode, mean, and median of the incentives. Since the mode is $12,000, one of the incentives is $12,000.
Let's assume the incentives received by the salesmen are: $x, $y, $z, $12,000, and $w.
Given that the mean and median are both $7000, we can say that the sum of all incentives is 5 * $7000 = $35,000.
From this, we can deduce that the total sum of the incentives excluding the $12,000 incentive is $35,000 - $12,000 = $23,000.
Therefore, the sum of the remaining four incentives (excluding $12,000) is $23,000, and the average of these four incentives is $7000.
Hence, the sum of the four incentives (excluding $12,000) is $28,000.
Now, we can find the difference between the highest and lowest incentive by subtracting $28,000 from $35,000:
$35,000 - $28,000 = $7,000
Therefore, the difference between the highest and lowest incentive received by the 5 salesmen is $7,000.
The mean and median of the incentives is $7000, and the only mode is $12,000. This information gives us an insight into the distribution of the incentives received by the 5 salesmen.
Difference between the Highest and Lowest Incentive
To find the difference between the highest and lowest incentive received by the salesmen, we need to consider the mode, mean, and median of the incentives. Since the mode is $12,000, one of the incentives is $12,000.
Let's assume the incentives received by the salesmen are: $x, $y, $z, $12,000, and $w.
Given that the mean and median are both $7000, we can say that the sum of all incentives is 5 * $7000 = $35,000.
From this, we can deduce that the total sum of the incentives excluding the $12,000 incentive is $35,000 - $12,000 = $23,000.
Therefore, the sum of the remaining four incentives (excluding $12,000) is $23,000, and the average of these four incentives is $7000.
Hence, the sum of the four incentives (excluding $12,000) is $28,000.
Now, we can find the difference between the highest and lowest incentive by subtracting $28,000 from $35,000:
$35,000 - $28,000 = $7,000
Therefore, the difference between the highest and lowest incentive received by the 5 salesmen is $7,000.
|
Explore Courses for GMAT exam
|
|
Top Courses for GMATView all
Question Description
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)$4000b)$13,000c)$9000d)$5000e)$11,000Correct answer is option 'E'. Can you explain this answer? for GMAT 2025 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about 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)$4000b)$13,000c)$9000d)$5000e)$11,000Correct answer is option 'E'. Can you explain this answer? covers all topics & solutions for GMAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 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)$4000b)$13,000c)$9000d)$5000e)$11,000Correct answer is option 'E'. Can you explain this answer?.
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)$4000b)$13,000c)$9000d)$5000e)$11,000Correct answer is option 'E'. Can you explain this answer? for GMAT 2025 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about 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)$4000b)$13,000c)$9000d)$5000e)$11,000Correct answer is option 'E'. Can you explain this answer? covers all topics & solutions for GMAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 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)$4000b)$13,000c)$9000d)$5000e)$11,000Correct answer is option 'E'. Can you explain this answer?.
Solutions for 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)$4000b)$13,000c)$9000d)$5000e)$11,000Correct answer is option 'E'. Can you explain this answer? in English & in Hindi are available as part of our courses for GMAT.
Download more important topics, notes, lectures and mock test series for GMAT Exam by signing up for free.
Here you can find the meaning of 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)$4000b)$13,000c)$9000d)$5000e)$11,000Correct answer is option 'E'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
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)$4000b)$13,000c)$9000d)$5000e)$11,000Correct answer is option 'E'. Can you explain this answer?, a detailed solution for 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)$4000b)$13,000c)$9000d)$5000e)$11,000Correct answer is option 'E'. Can you explain this answer? has been provided alongside types of 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)$4000b)$13,000c)$9000d)$5000e)$11,000Correct answer is option 'E'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice 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)$4000b)$13,000c)$9000d)$5000e)$11,000Correct answer is option 'E'. Can you explain this answer? tests, examples and also practice GMAT tests.
|
|
Explore Courses for GMAT exam
|
|
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
|
Signup to see your scores
go up
within 7 days!
within 7 days!
Takes less than 10 seconds to signup