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by ketkoag » Sat Mar 28, 2009 2:40 am
Martin has worked for the last 30 years. If his average (arithmetic mean) total annual
earnings for the first 5 years is $15,000, what is his average total annual earnings for the
last 5 years?
(1) Martin’s average total annual earnings for the first 25 years is $27,000.
(2) Martin’s average total annual earnings for the last 25 years is $34,000.

OA: C
I got the right answer. However, Please explain me the right method to solve this problem.
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Source: — Data Sufficiency |
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by DanaJ » Sat Mar 28, 2009 4:20 am
1 tells you that his average earnings for the first 25 years is 27 000. However, you don't have any info about his last 5 years and you are unable to determine his average earnings for the 30 years.

2 tells you that his average earnings for the last 25 years is 34 000. This means that, in his last 25 years of work, he earned 25*34 000. We are initially told that his average earnings for his first 5 years is 15 000, making his total earnings for this period of time 5*15 000. Using this info you can calculate his average earnings for the entire 30 years: (25*34 000 + 5*15 000)/30 = x (a certain amount, we're not necessarily interested in finding the exact number). However, this still isn't enough to determine what the problem is asking for.

But, put the two stmts together and you get that:
- you have the average for the 30 years from stmt 2 (that x)
- you have the average for the first 25 years from stmt 1 (27 000)
This means that you can now easily calculate the average for the last 5 years: (30x - 25*27 000)/5.
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