In a certain year the difference between Mary's and Jim's annual salaries was twice the difference between Mary 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
Average
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 NeilWatson
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 GMATGuruNY
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In ascending order, the salaries look like this: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.
JKM
According to the question stem:
MK = x.
MJ = 2x.
Thus, the salaries look like this:
JxKxM
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:
MJ = 2(MK)
MJ = 2M2K
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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 Brent@GMATPrepNow
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Let's first deal with the given information.NeilWatson wrote:In a certain year the difference between Mary's and Jim's annual salaries was twice the difference between Mary 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
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
 NeilWatson
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Perfect. Thanks. I completely missed the fact that K must be the average since its in the middle. I went straight into solving it algebraically and I messed up somewhere.
 DavidG@VeritasPrep
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We're told that Mary's salary is the highest. So if the gap between Mary and Jim's salary is larger than the gap between Mary and Kate's salary, then Jim must make less than Kate: JimKateMary.kovthe wrote:How did you figure the ascending order j,k,m?

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MJ=2(MK)
MJ==2M2k
2k=M+J
st 1= only salary of J is given we are not aware of M&K not sufficient
st 2= Value of k is given plus from above equation we know that M+J=2k
we have all the 3 values. Hence avg= M+J+K/3=80000+40000/3=avg
Statement 2 sufficient. AnswerB
MJ==2M2k
2k=M+J
st 1= only salary of J is given we are not aware of M&K not sufficient
st 2= Value of k is given plus from above equation we know that M+J=2k
we have all the 3 values. Hence avg= M+J+K/3=80000+40000/3=avg
Statement 2 sufficient. AnswerB

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Somehow I solved this in very easy manner.
From the question, we can write equation as below.
MJ = 2(MK) , So obviously J earns least .
M=2KJ
To find average salary, we need first total salary i.e. M+K+J
Substitute M =2KJ in above equation, we get Total salary = K
Now see at options ..
First one doesn't give info about k salary , whereas second one gives.. So answer is B.
From the question, we can write equation as below.
MJ = 2(MK) , So obviously J earns least .
M=2KJ
To find average salary, we need first total salary i.e. M+K+J
Substitute M =2KJ in above equation, we get Total salary = K
Now see at options ..
First one doesn't give info about k salary , whereas second one gives.. So answer is B.
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 Jay@ManhattanReview
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We have,NeilWatson wrote:In a certain year the difference between Mary's and Jim's annual salaries was twice the difference between Mary 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
M  J = 2(M  K)
=> M  J = 2M  2K
=> M = 2K  J
We have to find out the value of (M + K + J)/3.
Thus, (M + K + J)/3 = [(2K  J) + K + J]/3 = K.
Thus, we need to get the value K.
Only Statement 2 is sufficient.
The correct answer: B
Hope this helps!
Jay
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