Is q^r + 1 an odd number? (1) q + r is even (2) q is even

we are asked to determine whether \(q^r\) + 1 = odd or not.

Statement 1 :

q + r = even . This fact can be proved by 2 ways.

1. even + even = even . 2 +2 = 4
2. odd + odd = even . 3 + 1 = 4

If both q and r are even , we will always get odd number but the scenario is different when q and r are odd.

NOT sufficient.

Statement 2 :

This statement is a trap. anyone can say that if q is even \(q^r\) + 1 will be odd. But we don't sufficient information about r. Thus this statement becomes fruitless. r could be anything. so, NOT sufficient .

combining both statements:

if q is even r has to be even if we consider statement 1. even or odd can't be fraction .

So, both statements together are sufficient.

Thus the best answer is C.