Question

a prime number is any number greater than 1 that is divisible only by 1 and itself. ethan made a claim: the sum of any two prime numbers is an even number. what is a counterexample to this claim? 4 + 3 = 7 3 + 3 = 6 7 + 3 = 10 2 + 5 = 7

Explanation:

Step1: Identify valid prime pairs

First, check which options use only prime numbers:

• $4+3=7$: 4 is not prime, so invalid.
• $3+3=6$: Both 3 are primes.
• $7+3=10$: Both 7 and 3 are primes.
• $2+5=7$: Both 2 and 5 are primes.

Step2: Check sum parity

Find the pair whose sum is odd (to counter the "sum is even" claim):

• $3+3=6$: 6 is even, supports the claim.
• $7+3=10$: 10 is even, supports the claim.
• $2+5=7$: 7 is odd, contradicts the claim.

Answer:

D. $2 + 5 = 7$