Graduate Management Admission Test (GMAT) Practice Test

In mathematical operations, what is a common result for an odd number divided by an odd number?

1. Even integer

2. Odd integer

3. Non-integer

4. Both even and odd

The correct answer is: Non-integer

When you divide an odd number by another odd number, the result is not guaranteed to be an integer. To understand this, consider the form of odd numbers: any odd number can be expressed as \(2n + 1\), where \(n\) is an integer. Therefore, when an odd number \(a\) is divided by another odd number \(b\), the expression can be restructured as \((2n_1 + 1) / (2n_2 + 1)\). Given that both \(a\) and \(b\) might not share common factors, the division could yield a fraction that does not simplify to an integer. For example, if you were to divide 3 (which can be thought of as \(2(1) + 1\)) by 5 (or \(2(2) + 1\)), the result is \(3/5\), which is a non-integer. This analysis confirms that when you perform the division of one odd number by another, the outcome can often be a non-integer value, leading to the conclusion that option C is a common result in such scenarios.