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Average salary

by Nirupam04 » Fri Jul 05, 2013 3:57 am
Difference between Marry and Jim annual salary is twice the difference between Marry and Kate Annual salary. Marry salary is highest.
what is the average annual salary of 3 person.

1> JIM Annual salary 30K / Year
2> KAT annual salary 40L/ Year.

Please help to solve this question. Correct answer is B.
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by Brent@GMATPrepNow » Fri Jul 05, 2013 7:12 am
In a certain year, the difference between Mary's and Jim's annual salaries was twice the difference between Mary's and Kate's annual salaries. If Mary's annual salary was the highest of the 3 people, what was the average annual salary of the 3 people that year?
1. Jim's annual salary was $30,000 that year.
2. Kate's annual salary was $40,000 that year.
NOTE: I've posted the original question

NOTE: When posting questions, please use the spoiler function to hide the correct answer. This will allow others to attempt the question without seeing the final answer.


Let's first deal with the given information.
Let J = Jim's salary
Let M = Mary's salary
Let K = Kate's salary

Notice that the salaries (in ascending order) must be J, K, M
Also, if the difference between Mary's and Jim's annual salaries equals twice the difference between Mary's and Kate's annual salaries, then we can conclude that the 3 salaries are equally spaced.

Target question: What was the average annual salary of the 3 people that year?

Statement 1: Jim's annual salary was $30,000 that year.
In other words, J = 30,000
So, the three salaries, arranged in ascending order are: 30,000, K, M
Plus we know that the 3 salaries are equally spaced.
Do we now have enough information to answer the target question? No.

For proof that that we don't have enough information, consider these 2 cases:
Case a: J=30,000, K=30,001, M=30,002, in which case the average salary is $30,001
Case b: J=30,000, K=30,002, M=30,004, in which case the average salary is $30,002
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: Kate's annual salary was $40,000 that year.
In other words, K = 40,000
Perfect!
Since the 3 salaries are equally spaced, we can use a nice rule that says, "If the numbers in a set are equally spaced, then the mean and median of that set are equal"
Since Kate's salary must be the median salary, we now know that the average salary must be $40,000
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer = B

Cheers,
Brent
Last edited by Brent@GMATPrepNow on Fri Jul 05, 2013 7:13 am, edited 2 times in total.
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by GMATGuruNY » Fri Jul 05, 2013 7:13 am
In a certain year, the difference between Mary's and Jim's annual salaries was twice the difference between Mary's and Kate's annual salaries. If Mary's annual salary was the highest of the 3 people, what was the average annual salary of the 3 people that year?

1. Jim's annual salary was $30,000 that year.
2. Kate's annual salary was $40,000 that year.
In ascending order, the salaries look like this:
J-------------K-------------M

According to the question stem:
M-K = x.
M-J = 2x.
Thus, the salaries look like this:
J------x------K------x------M

The number line above implies that the salaries are EVENLY SPACED.
When values are evenly spaced, AVERAGE = MEDIAN.
The median salary here is the value of K.

Question rephrased: What is the value of K?

Statement 1: J=30,000.
Since different values of K are possible, INSUFFICIENT.

Statement 2: K=40,000
SUFFICIENT.

The correct answer is B.

Algebraic approach:

The average of the 3 salaries = (M+J+K)/3.

Since the difference between Mary's and Jim's annual salaries was twice the difference between Mary's and Kate's annual salaries, we get:
M-J = 2(M-K)
M-J = 2M-2K
2K = M+J.

Substituting M+J = 2K into (M+J+K)/3, we can rephrase the question stem as follows:
Average of the 3 salaries = (M+J+K)/3 = (2K + K)/3 = 3K/3 = K.

Question rephrased: What is the value of K?
From here, we can proceed as we did above.
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by bhakk » Sun Jul 07, 2013 8:47 pm
Thanks Mitch for solving it algebraically and thanks Brent for the the concept -If the numbers in a set are equally spaced, then the mean and median of that set are equal!!


GMATGuruNY wrote:
In a certain year, the difference between Mary's and Jim's annual salaries was twice the difference between Mary's and Kate's annual salaries. If Mary's annual salary was the highest of the 3 people, what was the average annual salary of the 3 people that year?

1. Jim's annual salary was $30,000 that year.
2. Kate's annual salary was $40,000 that year.
In ascending order, the salaries look like this:
J-------------K-------------M

According to the question stem:
M-K = x.
M-J = 2x.
Thus, the salaries look like this:
J------x------K------x------M

The number line above implies that the salaries are EVENLY SPACED.
When values are evenly spaced, AVERAGE = MEDIAN.
The median salary here is the value of K.

Question rephrased: What is the value of K?

Statement 1: J=30,000.
Since different values of K are possible, INSUFFICIENT.

Statement 2: K=40,000
SUFFICIENT.

The correct answer is B.

Algebraic approach:

The average of the 3 salaries = (M+J+K)/3.

Since the difference between Mary's and Jim's annual salaries was twice the difference between Mary's and Kate's annual salaries, we get:
M-J = 2(M-K)
M-J = 2M-2K
2K = M+J.

Substituting M+J = 2K into (M+J+K)/3, we can rephrase the question stem as follows:
Average of the 3 salaries = (M+J+K)/3 = (2K + K)/3 = 3K/3 = K.

Question rephrased: What is the value of K?
From here, we can proceed as we did above.
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