Graduate Management Admission Test (GMAT) Practice Test

What mathematical property can be inferred when adding multiple even numbers?

1. The sum is always odd

2. The sum is always even

3. The sum varies based on initial conditions

4. The sum results in prime numbers

The correct answer is: The sum is always even

When adding multiple even numbers, the mathematical property that can be derived is that the sum is always even. This stems from the definition of even numbers, which can be expressed in the form 2n, where n is an integer. When two even numbers are added together, say 2a and 2b, the result is: 2a + 2b = 2(a + b). Since a and b are integers, (a + b) is also an integer. Therefore, the sum can be expressed as 2 times another integer, which confirms that the result is still an even number. This principle holds true regardless of how many even numbers are being added; the sum will remain in the form of 2 times an integer, thus ensuring that it is even. This understanding is fundamental in number theory and arithmetic, especially when manipulating different types of integers. It provides a clear and consistent rule that applies in every scenario involving the addition of even numbers.