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B
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Difficulty:
55%
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Question Stats:
60% (01:52) correct
40%
(02:03)
wrong
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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 (arithmetic mean) annual salary of the 3 people that year7
(1) Jim's annual salary was $30,000 that year.
(2) Kate's annual salary was $40,000 that year.
(1) Jim's annual salary was $30,000 that year.
(2) Kate's annual salary was $40,000 that year.
26 Nov 2007, 00:53
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alimad
In a certain year, the difference between Mary's and Jim's annual salaries was twice the difference between Mary's and Kat's annual salaries. If Mary's annual salry was the highest of the 3 people, what was the average (arithmetic mean) annual salary of the 3 people that year?
Jim's annual salary was $30,000 that year
Kate's annual salary was $40,000 that year
M + J + K / 3 = ?
Statement I
M - 30,000 = 2(M-K) - Plug in Numbers
50,000 - 30,000 = 2 (50,000 - 40000)
20,000 = 200000
50+30 + 40 = 120/3 = 40,000
60,000 - 30,000 = 2 (60,000 - 45,000)
30,000 = 30,000
60+30 + 45 = 135 /3 = 4..... - insufficient
Statement II
M - J = 2 (M - 40,000)
Plug Numbers
50,000 - 30,000 = 2 (50,000 = 40,000)
50 + 40 + 30 = 120 /3 = 40 average
60,000 - 20,000 = 2( 60,000 - 40,000)
40,000 = 40,000
60 + 20 + 40 = 120/3 = 40 average --- Answer is B
This approach takes a long time. Please provide an alternative solution. Thanks
Jim's annual salary was $30,000 that year
Kate's annual salary was $40,000 that year
M + J + K / 3 = ?
Statement I
M - 30,000 = 2(M-K) - Plug in Numbers
50,000 - 30,000 = 2 (50,000 - 40000)
20,000 = 200000
50+30 + 40 = 120/3 = 40,000
60,000 - 30,000 = 2 (60,000 - 45,000)
30,000 = 30,000
60+30 + 45 = 135 /3 = 4..... - insufficient
Statement II
M - J = 2 (M - 40,000)
Plug Numbers
50,000 - 30,000 = 2 (50,000 = 40,000)
50 + 40 + 30 = 120 /3 = 40 average
60,000 - 20,000 = 2( 60,000 - 40,000)
40,000 = 40,000
60 + 20 + 40 = 120/3 = 40 average --- Answer is B
This approach takes a long time. Please provide an alternative solution. Thanks
Woah, slow down there killer. Thats too much work!
equation from stem: M-J=2(M-K) --> M-K=2M-2K --> M=2K-J
We want to know (M+J+K)/3
2K-J+J+K --> 3K/3 --> K is the average. If we know K then Suff.
So B is the answer.
Make sure to double check though to see if we can't get any others similar to 3K/3. ex/ maybe we can get 3J/3 or 4J/3 and so on... turns out we can't.
Updated on: 03 Oct 2020, 07:28
Originally posted by BrentGMATPrepNow on 30 Aug 2016, 07:52.
Last edited by BrentGMATPrepNow on 03 Oct 2020, 07:28, edited 2 times in total.
Last edited by BrentGMATPrepNow on 03 Oct 2020, 07:28, edited 2 times in total.
Kudos
Bookmarks
alimad
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 (arithmetic mean) annual salary of the 3 people that year7
(1) Jim's annual salary was $30,000 that year.
(2) Kate's annual salary was $40,000 that year.
(1) Jim's annual salary was $30,000 that year.
(2) Kate's annual salary was $40,000 that year.
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
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m+j+k) /3 =? that is 
