Number Properties
Number Properties Data Sufficiency problems test your ability to determine if given statements provide enough information about integer properties like divisibility, parity (even/odd), primality, and factors. You must assess sufficiency using number theory rules and logical deduction.
What You'll Learn
Introduction to Number Properties
Number Properties Data Sufficiency problems test your ability to determine if given statements provide enough information about integer properties like divisibility, parity (even/odd), primality, and factors. You must assess sufficiency using number theory rules and logical deduction.
Prerequisites
How to Solve Number Properties Problems
Step 1: Identify what is being asked (even/odd, prime, divisible, etc.)
Step 2: Translate each statement into number property conditions
Step 3: Check if Statement (1) alone gives a unique answer
Step 4: Check if Statement (2) alone gives a unique answer
Step 5: Combine statements if needed
Step 6: Test counterexamples to check sufficiency
Step 7: Select the appropriate DS answer choice
Example Problem
Example: Is integer n divisible by 6? Statement (1): n is divisible by 2. Statement (2): n is divisible by 3. Solution: Step 1: Question asks if divisible by 6 Step 2: Statement (1): n divisible by 2 → could be 2,4,6,8,... not all divisible by 6 → NOT sufficient alone Step 3: Statement (2): n divisible by 3 → could be 3,6,9,12,... not all divisible by 6 → NOT sufficient alone Step 4: Together: n divisible by both 2 and 3 → divisible by LCM(2,3)=6 → SUFFICIENT together Answer: Both statements together are sufficient
Pro Tips & Tricks
- Even/Odd: sum of two evens = even, odd+odd=even, even+odd=odd
- Product of any number with even = even
- For divisibility by 6: need divisibility by both 2 and 3
- For divisibility by 4: need last two digits divisible by 4
- Prime numbers > 2 are odd
- Remainder when divided by n: possible remainders are 0 to n-1
Shortcut Methods to Solve Faster
Common Mistakes to Avoid
Practice Worksheets
Practice makes perfect! Work through these worksheets to master Number Properties. Each worksheet contains 20 questions with detailed explanations. Start from Worksheet 1 and progress through increasing difficulty levels.
Exam Importance
Number Properties is an important topic for various competitive exams. Here's how frequently it appears:
Ready to Master Number Properties?
Start with Worksheet 1 and work your way up to expert level! Each worksheet includes: