Strategies, Sample Questions, and Random Ramblings.
July 19, 2015
Average is synonymous with mean/arithmetic mean and it is defined by a simple equation:
This equation will be the backbone to everything that we work on with GMAT averages, but there will be ways to simplify this as we move along. A basic example would be:
What is Dan’s average test score if he scored an 80, 85 and 96 on his three exams?
Now, 261 divided by 3 is not the end of world, but you can imagine how these numbers might get a little harder to handle if they started to get much larger. For this, we will make the average calculation a bit easier.
Averages are really just a relative term for two or more numbers. The average of 0 and 10 is 5, which is 5 away from each of the numbers. If we were to take the average of 2 other numbers that had a difference of 10, say 150 and 160, the average would still be only 5 away from each of these numbers at 155. What does that mean?
If you want to take the average of a group of large numbers you can first subtract the smallest number from all of the terms, find the average of your new terms and add that figure back to the number you subtracted in the beginning. That may sound complicated, but it will make perfect sense in an example. Let’s look at the original so that we can verify it works:
1) Subtract 80 from all of the terms to get 0, 5 and 16
2) Find the average of the new values
3) Add the average back to 80: 80 + 7 = 87
What you will find is that this method can keep you from working with unwieldy equations.
It is rare that you will be asked to compute a straight average; frequently data will be missing from the problem and you will have to figure it out. For example:
If Dan scored a 74, 75 and 76 on his first 3 exams, what would he need on his final exam to get an average of 80?
The traditional method would tell you to plug all of data into our equation like this:
An equation that you could solve like this:
Again, this math is not too difficult, but there is an easier way. Let’s break down what is happening when you take the average of 2 numbers. If you look at the average of 8 and 12, the answer (10) will probably pop into your head right away. However, you can think of the 12 as lending a number to 8 (2 in this case so that each term is equal). What this means is that you need to have the exact same absolute difference in values below your average than you do above. In the example with Dan, this means we have to have the same difference in numbers above 80 that we do below.
The difference for the first three terms are as follows:
This means that the last number needs to be 15 higher than 80 for the average to be 80. In this case, it is 80 + 15 = 95. No coincidence that the answers are the exact same. This method will save you time and make you a bit more accurate.
Another way to simplify and eliminate answer choices is to look at the ones digit in the equation. Because we know that the sum of the 4 exams will be 320 and the ones digit of the sum of the first three exams is 5, we then know that the ones digit of the final exam must be 5 as well. This method will likely eliminate 2 or 3 of the answer choices with very little math.
Greg R., client, New York City
Emil C., client, Singapore
Chris S, client, New York City