Strategies, Sample Questions, and Random Ramblings.
July 19, 2015
A weighted average is really just a type of average, but there is a bit different way that you can think about these types of problems that will be very helpful in many others. In fact, the methods used in this chapter will help you with with Rates, Work, and Mixture problems that we will discuss in the word problems section. Spend the time to understand it now, and you will be ahead of the game. The ability to handle gmat weighted averages quickly can free up 2-4 minutes on the exam for other problems.
If we had a problem where Dan scored 90 on three of his exams and an 80 on two of his exams we could figure out the average as we did before:
Or, we could simplify this a bit by factoring the numerator:
Either way you are going to get the same answer, but seeing this as a weighted average (the way the second one is written) will help solve some problems you will come across in a bit quicker fashion. In other words, what you are doing is summing the product of each value and its number of occurrences and dividing the result by the total occurrences.
In the above example, we can do the exact same calculation we did in the average chapter when subtracting the smallest value from each term and adding it back to the average. For our example, it will look like this:
This is because it is the weights and the difference between the numbers that matter, not the actual numbers themselves.
The method of reducing the numbers you are dealing with can also work with a more difficult problem as well:
If you had three sacks that weigh 95 pounds each and the average weight of 7 sacks is 87, what is the weight of the other 4?
First start with the basic equation:
Then subtract the smallest value, in this case 87 (remember the 2, 3, and 7 are weights), and solve for x. If you add -6 to 87 (the number we subtracted) you will get your answer of 81.
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