The word “average” on the GRE can refer to two concepts: arithmetic mean, and the average speed (or average rate) formula. It’s important not to confuse the two on the Test Day, as they require different formulas to solve.
Mean is the mathematical average. This is defined as the sum of the terms divided by the number of terms. Mean = Sum / # of terms. For a list of consecutive integers or evenly spaced numbers, the mean is equal to the median, or the middle number. For example, the “average” of 3, 5, and 9 is 5.67.
Average Speed or Average Rate is often found in complex word problems. This type of question is one many students are less familiar with so you may not have seen it before. Let’s review two important equations to remember and look at how this concept appears on the GRE.
The first formula to memorize is: D = R x T. This stands for Distance = Rate x Time (referred to as the “DIRT” formula). It is perfectly acceptable to also think of it as Time = Distance / Rate or as Rate = Distance / Time as well. Usually the “Rate” is speed but it could be anything “per” anything. In a word problem, if you see the word “per” you know this is a question involving rates.
The second formula is: Average Rate = Total Distance / Total Time. This is its own special concept and you will notice that it is NOT a simple Average of the Speeds (which would be something like the Sum of the Speeds / the Number of Different Speeds or what we know as the Arithmetic Mean). Average Rate is a completely different concept, so do not let the common word “average” confuse you. Let’s look at a sample question from Grockit’s GRE question bank:
Question 1: The average (arithmetic mean) of four numbers is 30, after one of the numbers is removed, the average of the remaining three numbers is 10. What number was removed?
We know that the four original numbers sum to 30*4 = 120. The new equation becomes:
4*30 – x/3 = 10
120 – x/3 = 10
120 – x = 30 (add an x to each side and subtract a 30)
90 = x