.The first thing to do for any GRE Average problem is to write down the average formula. Then, fill in any of the three variables (S, n, and A) that are given in the problem. For example:
The sum of 6 numbers is 90. What is the average term?
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The sum, S, is given as 90. The number of terms, n, is given as 6. |
| By plugging in, you can solve for the average:
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Notice that you do not need to know each term in the set to find the average.
Sometimes, using the average formula will be more involved. For example:
If the average of the list {2, 5, 5, 7, 8, 9, x} is 6.1, what is the value of x?
Plug the given information into the average formula, and solve for x:
More complex average problems involve setting up two average formulas. For example:
Sam earned a $2,000 commission on a big sale, raising his average commission by $100. If Sam’s new average commission is $900, how many sales has he made?
To keep track of two average formulas in the same problem, you can set up a Rate × Time = Distance (RTD)-style table. Instead of RT = D, Use A × n = S, which has the same form. Sam’s new average commission is $900, and this is $100 higher than his old average, so his old average was $800.
Note that the Number and Sum columns add up to give the new cumulative values, but the values in the Average column do not add up:
| Average | × | Number | = | Sum | |
| Old total | 800 | × | n | = | 800n |
| This sale | 2,000 | × | 1 | = | 2,000 |
| New total | 900 | × | n + 1 | = | 900(n + 1) |
The right-hand column gives the equation you need:
Remember: You are looking for the new number of sales, which is n + 1, so Sam has made a total of 12 sales.
The sum of 6 integers is 45. What is the average of the 6 integers?
The average price per item in a shopping basket is $2.40. If there are a total of 30 items in the basket, what is the total price of the items in the basket?