Number Properties are a critical component of GMAT Quant, testing your logical reasoning as much as your calculation skills. This guided path will teach you the core concepts and advanced strategies needed to master this topic.
Start with the fundamental types of numbers. This is the basic vocabulary for all Number Properties questions.
All rational and irrational numbers. They can be represented on a continuous number line.
Hover over points to see values.
Dive deeper into the most important number type—integers. Learn what makes them Prime, Even, Odd, and more with interactive examples.
Master the rules for adding, subtracting, and multiplying odd and even numbers—a key skill for logical deduction in Data Sufficiency.
Master the essential rules of divisibility (for 3, 4, 6, 8, 9, 11) and test your skills with our interactive checker.
Learn about prime factorization, how to find the total number of factors, and how to calculate the HCF of two numbers.
Every integer > 1 is a unique product of primes.
e.g., 12 = 2² × 3
If N = aᵖ × b^q, Total Factors = (p+1)(q+1).
Apply your knowledge to the GMAT's unique question type. Learn to evaluate sufficiency for questions about primes, factors, and remainders.
If x is an integer, is x a prime number?
(1) x is an even number.
(2) x is a factor of 14.
If x is even, it could be 2 (which is prime) or it could be 4, 6, 8, etc. (which are not prime). Since we get both a 'yes' and a 'no' answer, this is INSUFFICIENT.
The positive factors of 14 are 1, 2, 7, 14. x could be 2 or 7 (prime), or it could be 1 or 14 (not prime). INSUFFICIENT.
We need a number that is both even AND a factor of 14. The only even factors of 14 are 2 and 14.
If x=2, the answer is 'yes'. If x=14, the answer is 'no'. Since we still don't have a unique answer, it is INSUFFICIENT.
Final Answer: (E)
Explore special cases and number patterns (like ABAB or ABCABC) related to divisibility that can act as powerful shortcuts.
In any set of 'n' consecutive integers, exactly one number is divisible by 'n'. Try changing n and start.
Learn the formal algebraic method for solving complex remainder questions, a classic high-level GMAT problem type.
When N is divided by 7, remainder is 2. Find rem of 3N divided by 7.
Put your understanding of GMAT Number Properties: A Guide to Integer Logic to the test with our premium, adaptive practice questions. Build pacing efficiency and eliminate knowledge gaps now.
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.
Recursive sequences look scary, but they follow a pattern. Learn how to decode the definition and spot the hidden loop.