I think answer is "C"

Explanation -
Considering the following facts-
Odd*Odd=Odd
Odd*Even=Even
Even*Even=Even
Odd+Odd=Even
Odd +Even=Odd
Even+Even=Even


Now as per
1) a=Even where as b=Odd or Even hence INSUFFICIENT
2) a= Odd or Even, b= Odd or Even hence INSUFFICIENT
combining both
a=Even, b=Even

What is OA?

I would say answer is C

If a and b are integers, is b even?
(1) 3a + 4b is even.
to make 3a + 4b you must add odd+odd or even+even
4b is always even
but what about b? it can be odd or even, from (1) we only know that a is even
INSUFF

(2) 3a + 5b is even
even+even = even
to make 5b you must have b even
a is also even

odd+odd = even
5b must be odd, so b is odd
and a is odd
INSUFF

(1) and (2)
a-even so b is even

C

OA?

yes A+B can solve.
Ans must be C

IMO C

1) not sufficient
a b 3a+4b
e o e
e e e

2) 3a+5b=3a+4b+b
same drill, not sufficient

Both combined, 3a+4b+b=even and 3a+4b is even, b has to be even.

OA is C..Thanx Guys