Averages are a high-frequency topic on the GRE, testing your ability to reason with data sets. Top scores come from using conceptual shortcuts that are faster than the on-screen calculator. This path will teach you the core skills and strategies you need.
Start with the core definition of the Arithmetic Mean and use our interactive analyzer to see how Sum, Count, and Range are related.
Learn the most important strategy for solving average-based word problems: immediately converting an average into a Sum Total.
Whenever you see an Average, immediately calculate the Sum.
$$ \text{Sum} = \text{Avg} \times \text{Count} $$Master the concept of weighted averages for common GRE scenarios where some data points are more important than others.
Explore two powerful shortcuts: how averages behave when scaled, and how to instantly find the average of an arithmetic sequence.
Change the multiplier 'm' to see how the Average scales perfectly with it.
Learn the "surplus/deficit" method to solve QC average problems conceptually, which is much faster than direct calculation.
Old Avg 10 (n=5) -> Sum 50.
Add 16 -> New Sum 66 (n=6).
New Avg = 11.
Understand the definition of the Geometric Mean and the AM-GM inequality, a useful shortcut for certain advanced GRE problems.
The Geometric Mean (GM) is the nth root of the product.
$$ \text{GM} = \sqrt[n]{x_1 x_2 \dots} $$Key Rule (AM-GM): Arithmetic Mean ≥ Geometric Mean.
Put your understanding of GRE Averages: A Guide to Efficient Problem Solving to the test with our premium, adaptive practice questions. Build pacing efficiency and eliminate knowledge gaps now.
Stop calculating! Learn how to use the properties of symmetry to solve hard SD questions in seconds.
How to use 'Extreme Values' to find the range of a sum without calculating every fraction.
Forget formulas for a moment. Learn the 'Systematic Listing' method to build an unshakable intuition for Permutations & Combinations.