Consider the following statements:
I. The sum of any two odd numbers is always odd.
II. The product of any three consecutive natural numbers is divisible by 6.
Which of the above statements is/are correct?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → Only II
Test a property in general, not on one example: write an odd number as \(2k+1\) and look at what any run of consecutive numbers must contain.
I. The sum of any two odd numbers is always odd. — Incorrect. \((2a+1)+(2b+1)=2(a+b+1)\), which is even.
Example: \(3+5=8\), which is even
II. The product of any three consecutive natural numbers is divisible by 6. — Correct. Among any three consecutive numbers, at least one is even and one is a multiple of 3, so the product has the factors 2 and 3.
Example: \(4\times5\times6=120=6\times20\)
Example: \(7\times8\times9=504=6\times84\)