Which of the following statements about numbers is mathematically correct?
2026
Which of the following statements about numbers is mathematically correct?
Answer: A. The product of two even numbers is an even number — ConceptAn even integer has the form 2k, while an odd integer has the form 2k + 1, for some integer k. Parity is checked by divisibility by 2. A prime number…
- A.
The product of two even numbers is an even number
- B.
Every prime number is an even number
- C.
Zero is neither an even nor an odd number
- D.
The sum of two odd numbers is an odd number
Attempted by 141 students.
Show answer & explanation
Correct answer: A
Concept
An even integer has the form 2k, while an odd integer has the form 2k + 1, for some integer k.
Parity is checked by divisibility by 2. A prime number is an integer greater than 1 with exactly two positive divisors.
Application
Represent any two even integers as 2a and 2b.
Multiply them: (2a)(2b) = 4ab = 2(2ab).
The product has the form 2k with k = 2ab, so it is even.
Cross-check and contrast
For example, 2 multiplied by 6 equals 12, which is divisible by 2.
The statement that every prime number is even has the counterexample 3, which is prime and odd.
Zero equals 2 multiplied by 0, so zero is even rather than neither even nor odd.
For odd integers 2a + 1 and 2b + 1, the sum is 2(a + b + 1), which is even rather than odd.
Therefore, the mathematically correct statement is: The product of two even numbers is an even number.