Given that ๐ and ๐ are integers and ๐ + ๐2 ๐3 is odd, which one of the following statements is correct
Q. Given that ๐ and ๐ are integers and ๐ + ๐2 ๐3 is odd, which one of the following statements is correct?
| (A) ๐ and ๐ are both odd | (B) ๐ and ๐ are both even |
| (C) ๐ is even and ๐ is odd | (D) ๐ is odd and ๐ is even |
Ans: a is odd and b is even
Sol:
Given (a + a2b3) is odd
โ a (1 + ab3) is odd
As the multiplication of two numbers is odd only when those two numbers are odd.
That means โaโ is odd and (1 + ab3) is also odd
โ ab3 is even
As โaโ is an odd number, b3 should be even number to get ab3 as even.
b3 is even only when b is even.
Therefore, โaโ is odd and โbโ is even.