Given that 𝑎 and 𝑏 are integers and 𝑎 + 𝑎2 𝑏3 is odd, which one of the following statements is correct

Q. Given that 𝑎 and 𝑏 are integers and 𝑎 + 𝑎² 𝑏³ is odd, which one of the following statements is correct?

Ans: a is odd and b is even

Sol:

Given (a + a2b3) is odd

⇒ a (1 + ab3) is odd

As the multiplication of two numbers is odd only when those two numbers are odd.

That means ‘a’ is odd and (1 + ab3) is also odd

⇒ ab3 is even

As ‘a’ is an odd number, b3 should be even number to get ab3 as even.

b3 is even only when b is even.

Therefore, ‘a’ is odd and ‘b’ is even.