Graduate Management Admission Test (GMAT) Practice Test

If the sum of two prime numbers is even, what can we conclude about the primes?

1. Both primes are 2

2. Neither prime is 2

3. One prime is 2

4. Both can be odd

The correct answer is: Neither prime is 2

The statement that the sum of two prime numbers is even leads to a specific conclusion regarding the nature of the primes involved. In the realm of prime numbers, the only even prime is 2, while all other primes are odd. When two odd numbers are added, the result is always even. However, the sum of two odd primes would also yield an even number. This means that if both primes were odd, they could only result in an even sum. Consequently, if the sum is even, at least one of the primes has to be the even prime number—specifically, the number 2. Thus, if we are to sum two prime numbers and the result is even, we can definitively state that one of those primes must be 2. This aligns with the conclusion that if the prime sum is even, one prime number is indeed the even prime 2, ruling out the scenario where neither prime is 2. This leads us to conclude that option B is incorrect in this context. The correct reasoning identifies that one of the primes must be 2 for their sum to remain even, confirming option C as the valid conclusion.