There's a nice rule that says, "In a set where the numbers are equally spaced, the mean (average) will equal the median."[email protected] wrote:A machinist's salary at a factory increases by $2,000 at the end of each full year the machinist works. If the machinist's salary for the fifth year is $39,000, what is the machinist's average annual salary for his first 21 years at the factory?
Hi Brent,Brent@GMATPrepNow wrote:There's a nice rule that says, "In a set where the numbers are equally spaced, the mean (average) will equal the median."[email protected] wrote:A machinist's salary at a factory increases by $2,000 at the end of each full year the machinist works. If the machinist's salary for the fifth year is $39,000, what is the machinist's average annual salary for his first 21 years at the factory?
Here's an article I wrote about this property: https://www.beatthegmat.com/mba/2012/05/ ... d-the-mean
In this question, we have 21 years of salaries. Each year, the salary increases by $2000, so the yearly salaries might look something like this: $30000, $32000, $34000, $36000, etc
Since these salaries are equally spaced, the MEAN salary over the 21 year period will EQUAL the MEDIAN salary over the 21 year period.
The median salary will occur on the 11th year (the middlemost year).
We're told that in the 5th year, the salary $39,000
To find the salary in the 11th year, we'll add six increases of $2000 to get a salary of $51,000 in the 11th year
So, the mean salary = median salary = [spoiler]$51,000[/spoiler]
Cheers,
Brent
Nice Question.[email protected] wrote:A machinist's salary at a factory increases by $2,000 at the end of each full year the machinist works. If the machinist's salary for the fifth year is $39,000, what is the machinist's average annual salary for his first 21 years at the factory?
It's a very popular kind of series which appears on GMAT frequently. In the series here, the difference between two consecutive terms is a constant equal to 2000 (=2. In calculations, we can ignore 000) We don't know the first term of this series, but we know that its fifth term is 39000 (=39. In calculations, we can ignore 000). We only need to find its 1st and 21st terms, because the average of an evenly spaced sequence is simply the average of its 1st and last terms.[email protected] wrote:A machinist's salary at a factory increases by $2,000 at the end of each full year the machinist works. If the machinist's salary for the fifth year is $39,000, what is the machinist's average annual salary for his first 21 years at the factory?
