GRE Number Properties & Arithmetic: Quick Tricks & Tips

Why Number Properties Matter More Than You Think

Most GRE aspirants rush through number properties assuming they're "basic math." But here's the truth: nearly 30% of GRE Quant questions test your understanding of integers, divisibility, fractions, and ratios in disguised ways.

The difference between a 155 and a 165 often lies not in knowing advanced concepts, but in applying foundational arithmetic quickly and accurately.

Understanding Integers: The Building Blocks

Integers include all whole numbers—positive, negative, and zero. They exclude fractions and decimals.

Key properties you must remember:

Positive integers are greater than zero (1, 2, 3…). Negative integers are less than zero (−1, −2, −3…). Zero is neither positive nor negative—this trips up many test-takers.

Even and odd rules:

Even ± Even = Even

Odd ± Odd = Even

Even ± Odd = Odd

Even × Even = Even

Odd × Odd = Odd

Even × Odd = Even

These patterns show up constantly in GRE logic puzzles and inequality problems. Memorise them through practice, not passive reading.

Divisibility Rules You Can't Skip

Divisibility shortcuts save precious seconds during the exam.

Quick reference:

A number is divisible by 2 if its last digit is even. Divisible by 3 if the sum of its digits is divisible by 3. Divisible by 4 if its last two digits form a number divisible by 4. Divisible by 5 if it ends in 0 or 5. Divisible by 9 if the sum of its digits is divisible by 9.

For instance: Is 1,734 divisible by 3? Add the digits: 1 + 7 + 3 + 4 = 15. Since 15 is divisible by 3, so is 1,734.

This trick alone can help you eliminate wrong answer choices in seconds.

Prime Numbers and Factorisation

A prime number has exactly two factors: 1 and itself. The first few primes are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29.

Remember: 1 is not a prime number. 2 is the only even prime.

Prime factorisation breaks down numbers into prime multiples. For example, 36 = 2² × 3². This becomes essential when solving LCM and GCD problems, which appear frequently in ratio and data interpretation questions.

Fractions: Stop Overcomplicating Them

Fractions intimidate many aspirants unnecessarily. The key is practice and pattern recognition.

Simplification shortcut:

Always look for common factors before performing operations. For example, instead of calculating 48/72 directly, divide both by 24 to get 2/3.

Comparing fractions:

Cross-multiply to compare quickly. Which is larger: 5/8 or 7/11? Cross-multiply: 5 × 11 = 55 and 7 × 8 = 56. Since 56 > 55, 7/11 is larger.

Adding fractions with different denominators:

Find the least common denominator (LCD), convert, then add. But on the GRE, you can often estimate or use answer choices to eliminate options without full calculation.

Ratios and Proportions: Think in Parts

Ratios express relationships between quantities. If a ratio is 3:4, think of it as 3x and 4x, where x is a common multiplier.

Example: The ratio of boys to girls in a class is 5:7. If there are 60 students total, how many are boys?

Total parts = 5 + 7 = 12. Boys = (5/12) × 60 = 25.

This "parts method" works universally and reduces errors.

Proportions in real-world problems:

If 5 workers complete a task in 8 days, how long will 10 workers take? Set up the inverse proportion: 5 × 8 = 10 × x, so x = 4 days.

Percentages: The Shortcut Language

Percentages are just fractions in disguise. Converting between fractions, decimals, and percentages should be automatic.

Common conversions to memorise:

1/2 = 50% | 1/3 ≈ 33.33% | 1/4 = 25% | 1/5 = 20% | 1/8 = 12.5% | 1/10 = 10%

Percent increase/decrease formula:

(Change / Original) × 100

For quick mental math, use approximations. If something increases from 80 to 92, that's roughly a 15% increase without exact calculation.

Arithmetic Shortcuts That Actually Save Time

Multiplying by 5: Multiply by 10, then divide by 2.

Squaring numbers ending in 5: For 35², take 3 × 4 = 12, then append 25. Answer: 1,225.

Doubling and halving: To multiply 16 × 25, think 8 × 50 = 400.

These aren't gimmicks. They're cognitive load reducers that free up mental energy for harder problems.

Some aspirants find it easier to internalise these tricks through timed drills on platforms like PrepAiro, where pattern recognition builds naturally through repetition.

Common Mistakes to Avoid

Forgetting that zero is even. Assuming all integers are positive. Mixing up "at least" and "at most" in inequality problems. Dropping negative signs during simplification. Not simplifying fractions before performing operations.

Track your error patterns. Most mistakes aren't random—they're recurring blind spots that targeted practice can fix.

Building Speed Without Sacrificing Accuracy

Speed comes from recognition, not rushing. When you've solved 50 divisibility problems, the 51st becomes automatic.

Start with untimed accuracy. Once your accuracy crosses 80%, introduce time pressure gradually. Use estimation aggressively—GRE rewards smart approximation.

Review wrong answers immediately, not in bulk. Understanding why you missed a question matters more than the number of questions you attempt.

Final Thoughts

Number properties and arithmetic form the invisible foundation of GRE Quant success. These aren't topics you master once and forget—they're skills you sharpen through consistent, deliberate practice.

The aspirants who score high don't necessarily know more formulas. They simply apply foundational concepts faster, cleaner, and with fewer mistakes. That fluency comes from practice that's both structured and reflective.

Your goal isn't to memorise every rule perfectly. It's to internalise the patterns so deeply that solving becomes instinctive. Start small, stay consistent, and let mastery build gradually.

FAQ Section

Q1: What are the most important number properties for GRE Quant?

Focus on even/odd rules, divisibility shortcuts (especially for 3, 4, 5, 9), prime factorisation, and properties of zero. These appear in 30–40% of quant questions, often in disguised forms.

Q2: How do I improve my speed with fractions and ratios?

Memorise common fraction-to-percentage conversions, practice cross-multiplication for comparisons, and use the "parts method" for ratio problems. Speed comes from pattern recognition through timed practice.

Q3: Are arithmetic shortcuts really worth learning for the GRE?

Absolutely. Shortcuts like squaring numbers ending in 5, multiplying by 5, and doubling/halving reduce cognitive load and save 10–15 seconds per problem, which compounds across the exam.

Q4: What's the biggest mistake students make with number properties?

Treating them as "easy" and skipping focused practice. Most errors come from careless mistakes with negatives, zero, or even/odd properties—issues that only surface under timed pressure.

Q5: How much time should I spend on arithmetic fundamentals?

Dedicate 7–10 days to building strong foundations, then integrate these concepts into broader quant practice. Revisit fundamentals weekly to maintain fluency.

Q6: Can I use a calculator for GRE arithmetic questions?

Yes, the GRE provides an on-screen calculator, but it's often slower than mental math for simple operations. Use it strategically for complex decimals or large multiplications, not basic arithmetic.