The GMAT would provide answer choices, as shown below:
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?
9
10
11
12
13
Since the new average commission of $900 raises Sam's previous average commission by $100, his previous average commission = 900-100 = $800.
Thus:
Average commission for the previous sales = 800.
Average commission for the last sale = 2000.
Average commission for the MIXTURE of all the sales = 900.
This is a MIXTURE problem.
To determine the total number of sales, we can use ALLIGATION.
Step 1: Plot the 3 averages on a number line, with the average for the previous sales and that for the last sale on the ends and the average for the mixture in the middle.
800---------------------900-----------------2000
Step 2: Calculate the distances between the averages.
800---------
100--------900--------
1100------2000
Step 3: Determine the ratio in the mixture.
The required ratio of $800 sales to $2000 sales is equal to the RECIPROCAL of the distances in red.
($800 sales) : ($2000 sales) = 1100:100 = 11:1.
The resulting ratio implies that there are 11 sales with an average commission of $800 and 1 sale with a commission of $2000, for a total of 12 sales.
The correct answer is
D.
An alternate approach is to PLUG IN THE ANSWERS, which represent the total number of sales.
When the correct answer choice is plugged in, the commission for the last sale will be $2000.
Answer choice D: 12 sales
Since the average commission for all 12 sales = $900, the sum of the commissions for all 12 sales = 12*900 = 10,800.
Since the average commission for all but the last sale = $800, the sum of the commissions for the previous 11 sales = 11*800 = 8800.
Commission for the last sale = (sum of the commissions for all 12 sales) - (sum of the commissions for the previous 11 sales) = 10,800 - 8800 = 2000.
Success!
The correct answer is
D.
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