Introduction to GMAT Arithmetic (with Practice Tips)

Why Arithmetic is the Heart of GMAT Quant

When you hear 'GMAT Quant,' you might think of complex algebra. But the reality is that Arithmetic and its close cousin, Number Properties, form the bedrock of the section, accounting for a majority of the questions. The GMAT doesn't test your ability to do complex calculations; it tests your ability to reason with the fundamental properties of numbers. Mastering these concepts is non-negotiable for a high score.

Number Properties: The Rules of the Game

Number Properties is the most frequently tested topic within GMAT Quant because it's all about logic and rules. It covers the characteristics of integers, such as:

• Odd & Even Numbers: Understanding how odd and even numbers behave in addition, subtraction, and multiplication.
• Positive & Negative Numbers: Knowing the rules for multiplying and dividing positive and negative numbers.
• Integers vs. Non-integers: The GMAT is very precise with its language. If a question states 'x is an integer,' you know it cannot be a fraction or a decimal.
• Factors, Multiples, and Divisibility: You must know the definitions of factors and multiples, and the rules of divisibility (e.g., a number is divisible by 3 if the sum of its digits is divisible by 3).
• Prime Numbers & Prime Factorization: Prime numbers are the building blocks of all integers. Breaking a number down into its prime factors is a key skill for solving a wide range of problems, especially those involving divisibility, LCM, and GCD.

Fractions, Decimals, and Percents: The Triple Threat

These three concepts are just different ways of expressing the same value, and the GMAT expects you to be fluent in converting between them. Mastering them is crucial for a huge variety of word problems.

• Fractions: Be comfortable with adding, subtracting, multiplying, and dividing fractions. A key skill is learning to compare fractions quickly using methods like cross-multiplication or converting them to decimals.
• Decimals: Know how to perform basic operations with decimals and understand the concept of terminating versus repeating decimals.
• Percents: This is a huge topic on the GMAT, especially in word problems involving discounts, interest, and growth. You must know the formulas for percentage increase and decrease inside and out.

Ratios and Proportions: The Art of Comparison

Ratios and proportions are a specific type of comparison that appears frequently in GMAT word problems. They test your ability to understand the relationship between different quantities. For example, if the ratio of boys to girls in a class is 3:2 and there are 18 boys, how many students are there in total? You'll need to set up and solve a proportion to find the answer.

Common Arithmetic Traps to Avoid

1. Forgetting About Zero and One: Zero is an even integer, and one is a factor of every integer. These special cases are often used to create trap answer choices.
2. Assuming Numbers are Integers: Unless a question explicitly states that a variable is an integer, it could be a fraction. Don't make assumptions!
3. The Square Root Trap: If x² = 16, x could be 4 or -4. Forgetting the negative possibility is a classic GMAT trap.
4. Percent Of vs. Percent Greater Than: '150% of x' is very different from '150% greater than x.' Read the language of percent questions very carefully.

Worked examples: the three arithmetic traps in action

These three examples cover the GMAT arithmetic traps that cause the most wrong answers — each demonstrates a specific reasoning error and the correct mental move to avoid it.

Example 1: The zero and one trap

Question: If n is a positive integer and n² = n, what is the value of n?

Common wrong answer: Students assume n must be greater than 1 and try values like 2, 3, 4. None work. Correct approach: n² = n means n² − n = 0, so n(n−1) = 0. Therefore n = 0 or n = 1. Since n must be a positive integer, n = 1. The "n = 1 is special" property is the answer. This question type appears 3–4 times per official practice test in various disguises.

Example 2: The percentage base trap

Question: A store raises the price of a jacket from $80 to $100. By what percentage did the price increase?

Common wrong answer: 20% (calculating $20/$100). Correct approach: Percent change always uses the ORIGINAL value as the base. Change = $20. Base = $80 (the original price). Percentage increase = 20/80 = 25%. If you used $100 as the base, you got 20% — the classic "wrong base" trap answer that GMAC deliberately includes as a choice.

Example 3: The integer assumption trap

Question: If x > 0 and x² < x, which of the following must be true? (A) x > 1 (B) x < 1 (C) x = 0.5 (D) x is an integer (E) x > 0.5

Common wrong answer: Students try x = 2, get 4 < 2 = false, try x = 0.5, get 0.25 < 0.5 = true, and choose (C) thinking x must equal 0.5. Correct approach: x² < x with x > 0 means dividing by x gives x < 1. Combined with x > 0, we get 0 < x < 1. Any value between 0 and 1 works — x could be 0.3, 0.7, 0.99. So (B) "x < 1" must be true. (C) is not "must be true" — x = 0.5 is only one possibility. Answer: (B). The key is "must be true" does not mean "could be true."