Q. Given that 𝑎 and 𝑏 are integers and 𝑎 + 𝑎2 𝑏3 is odd, which one of the following statements is correct?
| (A) 𝑎 and 𝑏 are both odd | (B) 𝑎 and 𝑏 are both even |
| (C) 𝑎 is even and 𝑏 is odd | (D) 𝑎 is odd and 𝑏 is even |
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.
