Understanding Positive and Negative Numbers & Absolute Value for GMAT
Mastering positive and negative numbers, along with the concept of absolute value, is fundamental for success on the GMAT's Quantitative Reasoning section. These concepts form the bedrock for more complex arithmetic, algebraic manipulations, and problem-solving strategies.
Positive and Negative Numbers: The Number Line
Numbers can be categorized as positive, negative, or zero. The number line is a visual tool that helps us understand their relationships. Positive numbers are to the right of zero, while negative numbers are to the left. The further a number is from zero, the greater its magnitude.
Absolute Value: Distance from Zero
The absolute value of a number is its distance from zero on the number line, regardless of direction. It is always a non-negative value. The symbol for absolute value is two vertical bars, e.g., |x|.
The absolute value of a number 'x', denoted as |x|, represents its distance from zero on the number line. For any real number x:
- If x is positive or zero (x ≥ 0), then |x| = x.
- If x is negative (x < 0), then |x| = -x (which makes it positive).
For example:
- |5| = 5 (since 5 is positive)
- |-5| = 5 (since -5 is negative, its absolute value is -(-5) = 5)
- |0| = 0
This concept is vital when dealing with differences between numbers or when a quantity must be positive, such as a measure of length or time.
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Applying Concepts in GMAT Problems
GMAT quantitative problems often test your understanding of these fundamentals through word problems, number properties, and algebraic equations. Pay close attention to signs and the definition of absolute value when solving.
Remember: Absolute value is always non-negative. It's about distance, not direction.
10 - 7 = 3
Practice Scenarios
Consider a scenario where a company's profit is -500). The absolute value of this profit is |-500| = $500. This represents the magnitude of the financial outcome, irrespective of whether it was a gain or a loss.
Another example: If a submarine is at a depth of 100 meters below sea level, its position can be represented as -100 meters. Its distance from sea level (its absolute depth) is |-100| = 100 meters.
Learning Resources
The official guide from the Graduate Management Admission Council provides comprehensive coverage of GMAT math topics, including number properties and absolute value, with practice questions.
This section offers a structured learning path with videos and practice exercises on negative numbers, their properties, and the concept of absolute value.
A detailed explanation of absolute value with GMAT-specific examples and common pitfalls to avoid.
This blog post from Manhattan Prep covers essential number properties relevant to the GMAT, including integers, positives, and negatives.
A clear and concise explanation of absolute value, including how it appears in GMAT problems and strategies for solving them.
A video tutorial demonstrating how to solve GMAT problems involving absolute value, with step-by-step explanations.
A comprehensive overview of the mathematical concept of absolute value, its properties, and applications.
A foundational article on integers, including positive and negative numbers, which is crucial for understanding absolute value.
An introductory guide to number properties for the GMAT, covering integers, positive and negative numbers, and their operations.
A lesson focusing on absolute value, including its definition, properties, and how to solve equations and inequalities involving it.