Mastering Number Properties for Quantitative Reasoning (GRE)
Quantitative Reasoning on the GRE tests your ability to understand, interpret, and analyze quantitative information. A strong grasp of number properties is fundamental to solving a wide range of problems efficiently. This module will equip you with the essential knowledge of number types, divisibility rules, prime numbers, and their applications in problem-solving.
Understanding Number Classifications
Numbers can be categorized into various sets, each with unique characteristics. Knowing these classifications helps in identifying patterns and applying specific rules.
Yes, -5 is a rational number because it can be expressed as the fraction -5/1.
Divisibility Rules: Shortcuts to Efficiency
Divisibility rules are shortcuts to determine if a number can be evenly divided by another number without performing long division. Mastering these rules can save significant time on the GRE.
| Number | Rule | Example |
|---|---|---|
| 2 | The number is even (ends in 0, 2, 4, 6, or 8). | 124 is divisible by 2. |
| 3 | The sum of the digits is divisible by 3. | 345 (3+4+5=12) is divisible by 3. |
| 4 | The last two digits form a number divisible by 4. | 716 (16 is divisible by 4) is divisible by 4. |
| 5 | The number ends in 0 or 5. | 230 is divisible by 5. |
| 6 | The number is divisible by both 2 and 3. | 432 is divisible by 2 and 3, so it's divisible by 6. |
| 9 | The sum of the digits is divisible by 9. | 819 (8+1+9=18) is divisible by 9. |
| 10 | The number ends in 0. | 560 is divisible by 10. |
Remember that divisibility by 7, 11, and 13 are less commonly tested directly but understanding prime factorization is key.
Prime Numbers and Prime Factorization
Prime numbers are the building blocks of integers. Understanding them and how to find their prime factors is crucial for many GRE math problems, especially those involving LCM, GCF, and number theory.
Visualizing the process of prime factorization helps in understanding how composite numbers are built from primes. Imagine a factor tree where each branch splits a composite number into two factors until only prime numbers remain at the end of each branch. For instance, to factor 36: Start with 36. Branch into 6 and 6. Each 6 branches into 2 and 3. The prime factors are 2, 2, 3, 3. This visual representation reinforces the concept of unique prime factorization.
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The prime factorization of 60 is (or ).
Even and Odd Numbers
The distinction between even and odd numbers is fundamental and has predictable rules when performing arithmetic operations.
| Operation | Even + Even | Odd + Odd | Even + Odd | Even x Even | Odd x Odd | Even x Odd |
|---|---|---|---|---|---|---|
| Result | Even | Even | Odd | Even | Odd | Even |
These rules are crucial for quickly determining the parity (evenness or oddness) of results in complex calculations, especially when variables are involved.
Key Concepts for GRE Application
Understanding these number properties allows you to tackle various GRE question types more effectively.
a * b is even (Odd x Even = Even). Even + a (Odd) = Odd. So, the result is Odd.
Learning Resources
Official GRE math review from ETS, covering fundamental number properties relevant to the exam.
A comprehensive overview of number properties with GRE-specific examples and tips from Kaplan.
In-depth video lessons and practice exercises on number theory, including primes, divisibility, and more.
A detailed explanation of number properties with a focus on GRE strategies and common pitfalls.
An encyclopedic resource defining prime numbers, their properties, and related concepts.
A clear and visual explanation of divisibility rules for various numbers.
A playlist of video tutorials covering various aspects of number properties for GRE preparation.
A mathematical explanation of the unique prime factorization theorem.
Practice questions specifically designed to test your understanding of number properties on the GRE.
A lesson explaining the different sets of numbers, including integers, rational, and irrational numbers.