Math Problem Statement

Kim says that the sum of two prime numbers is always even. Which of the statements below shows that Kim is not correct?

Solution

Let’s analyze the problem from the uploaded image.

Kim claims that the sum of two prime numbers is always even. We are tasked with identifying which statement disproves this claim.

Key point:

  • A prime number is a number greater than 1 that has only two divisors: 1 and itself.
  • Most prime numbers are odd, except for 2, which is the only even prime number.

The sum of two odd numbers is always even. However, if one of the prime numbers is 2 (even), and the other is odd, their sum will be odd, disproving Kim's claim.

Now, let's evaluate the options:

Option A: 7 + 5 = 12

  • Both 7 and 5 are prime numbers.
  • Their sum is 12, which is even.
  • This does not disprove Kim's claim.

Option B: 3 + 8 = 11

  • 3 is a prime number, but 8 is not prime (it's divisible by 2 and 4).
  • This does not meet the criteria for testing the claim, as both numbers must be prime.

Option C: 2 + 11 = 13

  • 2 is a prime number (the only even prime), and 11 is also a prime number.
  • Their sum is 13, which is odd.
  • This disproves Kim's claim, as it provides a counterexample showing the sum of two prime numbers can be odd.

Option D: 2 + 9 = 11

  • 2 is a prime number, but 9 is not prime (it's divisible by 3).
  • This does not meet the criteria for testing the claim.

Conclusion:

The correct answer is C: 2 + 11 = 13, as it shows Kim's claim is not correct.

Would you like further clarification on this?


Here are 5 related questions to expand your understanding:

  1. What is the definition of a prime number?
  2. Why is 2 considered the only even prime number?
  3. How can you prove that the sum of two odd numbers is always even?
  4. Can a prime number ever be negative?
  5. What are some examples of sums of two prime numbers that are even?

Tip: Remember, counterexamples are a powerful way to disprove general statements in mathematics!

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Math Problem Analysis

Mathematical Concepts

Prime Numbers
Odd and Even Numbers

Formulas

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Theorems

Properties of Prime Numbers

Suitable Grade Level

Grades 6-8