Graduate Management Admission Test (GMAT) Practice Test

Why is the sum of two odd prime numbers always odd?

1. One of the primes is 2

2. Both primes are odd

3. 2 is not an odd number

4. Even + Odd = Odd

The correct answer is: Both primes are odd

The reason that the sum of two odd prime numbers is always even is because both numbers being added are odd. In mathematics, odd numbers can be expressed in the form of 2n + 1, where n is any integer. For example, the odd prime numbers include 3, 5, 7, and 11, which can all be represented in this form. When you add two odd numbers together, such as (2n + 1) and (2m + 1), where n and m are integers, the sum can be simplified as follows: (2n + 1) + (2m + 1) = 2n + 2m + 2 = 2(n + m + 1) The resulting expression is clearly an even number, as it can be factored into 2 times another integer (n + m + 1). This demonstrates that the sum of two odd numbers is always even. In the context of the answer choice, the option stating that both primes are odd directly supports the conclusion that their sum is even, as it highlights the essential property of odd numbers that leads to this result.