GMAT Averages: A Guide to Logical Problem Solving

Averages are a core concept on the GMAT, testing your ability to work logically with sets of data. Success requires moving beyond simple calculation to master weighted averages and the unique demands of Data Sufficiency. This guided path will build that expertise.

Section 1: The Core Toolkit

The Foundation: What is an Average?

Start with the core definition of the Arithmetic Mean and use our interactive analyzer to see how Sum, Count, and Range are related.

Interactive Data Set Analyzer

The #1 GMAT Skill: Working with Sums

Learn the most important strategy for solving average-based word problems: immediately converting an average into a Sum Total.

Step 1The Core Inference

Whenever you see an Average, immediately calculate the Sum.

$$ \text{Sum} = \text{Avg} \times \text{Count} $$

Step 2Example 1

Given: Class of 20 students, Avg Age 14.
Infer: $$ \text{Total Age} = 20 \times 14 = 280 $$

Step 3Example 2

Given: Avg daily visits in June is 120.
Infer: $$ \text{Total Visits} = 120 \times 30 = 3600 $$ (June has 30 days).

Section 2: GMAT-Specific Concepts & Applications

Application: Weighted Averages

Master the concept of weighted averages for common GMAT scenarios where some data points are more important than others.

Step 1The Formula

When values have different weights (frequencies):
$$ \text{Avg} = \frac{w_1 x_1 + w_2 x_2}{w_1 + w_2} $$

Step 2Scenario: Class Scores

24 students get 60, 16 get 70, 10 get 80.
$$ \frac{(24 \times 60) + (16 \times 70) + (10 \times 80)}{50} = 67.2 $$

Step 3Scenario: Stock Price

10 shares at $50, 40 shares at $60.
$$ \frac{(10 \times 50) + (40 \times 60)}{50} = \$58 $$

Data Sufficiency with Averages

Apply your knowledge to the most unique GMAT question type. Learn to analyze average statements for sufficiency without calculating.

Q: Avg of 5 numbers?
(1) Min is 10.
(2) Range is 20.

Analysis: Neither statement gives the Sum. Even combined, we only know Min and Max, not the middle numbers. Answer: E

Special Properties & Shortcuts

Explore two powerful shortcuts: how averages behave when scaled, and how to instantly find the average of an arithmetic sequence (mean = median).

Multiply entire set by 'm'

Change the multiplier 'm' to see how the Average scales perfectly with it.

Conceptual Topic: The Geometric Mean

Understand the definition of the Geometric Mean and the AM-GM inequality, a useful shortcut for certain advanced GMAT 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.

Interactive Practice

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