Graduate Management Admission Test (GMAT) Practice Test

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What will the output be when adding an odd number to an even number?

Even
Odd
Zero
None

The correct answer is: Odd

When an odd number is added to an even number, the result is always an odd number. This is because an even number can be described as being divisible by 2, while an odd number is one more than an even number. To understand this further, consider an even number as $2k$ (where $k$ is an integer) and an odd number as $2m + 1$ (where $m$ is also an integer). When you perform the addition: \[ (2k) + (2m + 1) = 2k + 2m + 1 = 2(k + m) + 1 \] The expression $2(k + m)$ indicates an even number, and adding 1 to it makes the total odd. Therefore, the sum of an odd number and an even number will always yield an odd result. This confirms that the output of adding an odd number to an even number is indeed odd.