Tips and Tricks for Even & Odd Questions | Quantitative for GMAT PDF Download

Breaking down a number into its prime factors is a valuable skill on the GMAT. To create a prime factor tree, start by identifying numbers that evenly divide into the given number. For instance, with the number 72, test different divisors until finding one that divides without leaving a remainder. Once such a divisor is found, split the number into factors. For example, since 72 is divisible by 6, it can be split into 6 and 72 ÷ 6, which is 12. Repeat this process for 6 and 12 until each branch on the tree ends with a prime number. Continue until only prime numbers remain, as prime numbers cannot be split further. In the case of 72, it breaks down into 5 prime factors (including repeats): 2 × 3 × 2 × 2 × 3.

The GMAT emphasizes understanding the factor foundation rule, which states that if a is a factor of b, and b is a factor of c, then a is a factor of c as well. In simpler terms, any whole number is divisible by all its factors, and it's also divisible by the factors of those factors. For example, if 72 is divisible by 12, then 72 is also divisible by all the factors of 12, including 1, 2, 3, 4, 6, and 12. This rule allows you to view factors as essential building blocks forming a foundation. For instance, 12 and 6 are factors, or building blocks, of 72 because 12 × 6 equals 72.

Moreover, the number 12 is constructed from its own factors, such as 4 × 3 building 12. Consequently, if 12 is part of the foundation of 72 and 12 is built from its prime factors (2, 2, and 3), then 72 is also constructed on the foundation of 2, 2, and 3.

Taking it a step further, almost any factor of 72 can be built using the bottom level of the foundation. For instance, 8 is a factor of 72 because you can create 8 using the three 2's in the bottom row (8 = 2 × 2 × 2). However, there is an exception – the number 1 cannot be constructed from the building blocks in the foundation. Despite not being prime, 1 is a factor of every integer. With this exception, every factor of 72 can be constructed using the lowest level of the building blocks in its foundation.

Even-Odd concepts in GMAT Quant are considered relatively straightforward, but students often struggle with them, especially in more challenging 700+ level questions. Our Subject Matter Experts have closely analyzed the mistakes students make in Even-Odd questions, drawing insights from internal forums and the errors of over 2000 students in our live classrooms on Number Properties.

To help you understand this topic better, we've outlined three common pitfalls in GMAT Quant Even-Odd questions, along with tips on how to avoid them. We've also provided illustrative GMAT Number Properties (Odd-Even) questions for practice.
Here are the key points:

3 Primary Pitfalls of GMAT Quant Even-Odd Questions

1. Getting intimidated by complex expressions:

What it means: Some Even-Odd questions may present intimidating expressions, causing anxiety and potential mistakes.
How to avoid: Remind yourself that GMAT Quant questions can be elegantly simplified. Even complex-looking questions can be broken down into simpler cases.
Illustrative Example: For instance, consider the expression (j³-27)²(j³+1)³. Instead of panicking, recognize that the even-odd nature remains unchanged when raising a number to a power. Simplify step by step, reducing the question to the basic inquiry: Is j even?

2. Wasting time on unimportant terms:

What it means: Spending too much time on terms that don't contribute to determining the even-odd nature of the overall expression.
How to avoid: Focus on the crucial terms that influence the even-odd nature of the entire expression. Break down the problem into smaller, manageable parts.

3. Getting stumped in division:

What it means: Difficulty arises when dealing with division in Even-Odd questions.
How to avoid: Break down the division step by step, examining the even-odd nature of individual terms involved. Simplify the problem to fundamental questions about the even-odd nature of individual factors.

Takeaways

• Utilize Even-Odd combinations to simplify complex expressions.
• Approach each question with confidence, knowing that GMAT questions can be simplified elegantly.
• Avoid being intimidated by complex expressions, and resist the urge to apply unnecessary algebraic formulas.

In essence, the key is to break down seemingly complicated Even-Odd questions into simpler components and approach them methodically. This step-by-step process allows for a clearer understanding and increases the likelihood of arriving at the correct answer.