Graduate Management Admission Test (GMAT) Practice Test

If a prime number is involved in an operation and results in an even sum, which of the following must be true?

1. Both numbers are odd

2. At least one number must be 2

3. Both must be even

4. It can never be true

The correct answer is: At least one number must be 2

In the context of prime numbers and their sums, when assessing the scenario of achieving an even sum, we need to consider the properties of even and odd numbers. A prime number is defined as a natural number greater than 1 with no positive divisors other than 1 and itself. The only even prime number is 2; all other prime numbers (3, 5, 7, etc.) are odd. For the sum of two numbers to be even, there are a couple of logical combinations: - **Even + Even = Even** - **Odd + Odd = Even** Since there is only one even prime (which is 2), if a prime number is involved in generating an even sum, at least one of the addends must involve the number 2. If 2 is used in addition with any odd prime (or another even number, though that can be distinctly indicated here), the sum will yield an even outcome. Thus, it must hold true that at least one of the numbers involved in the operation must be the prime number 2 whenever the sum is even. This reasoning clarifies why the correct answer indicates that at least one number must be 2, as it is the only even prime eligible