Odd x Odd = Odd
Odd x Even = Even
Even x Even = Even

To fulfill condition Either (A+1) or (B+1) needs to be Even
So either A or B needs to be odd
Or Atleast one of them is odd.

Ans C. At least one of them is odd.

Good luck
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(A+1)(B+1)=even; if A or B is odd . odd+1 is even. any number multiplied by even is even. So C.

C

for (A+1)(B+1) to be even there are three cases:

e*o=>(o+1)(e+1)
e*e=>(o+1)(o+1)
o*e=>(e+1)(o+1)

hope it helps

(A+1)(B+1) is even means that either A+1 or B +1 is even.

And if either A+1 or B +1 is even, then either A or B is odd because adding 1 will give us one even expression.

Hence C is the answer
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Another approach is to systematically test all 4 possible cases:

case a: A is EVEN and B is EVEN
The expression (A+1)(B+1) becomes (EVEN+1)(EVEN+1) = (ODD)(ODD) = ODD

case b: A is EVEN and B is ODD
The expression (A+1)(B+1) becomes (EVEN+1)(ODD+1) = (ODD)(EVEN) = EVEN

case c: A is ODD and B is EVEN
The expression (A+1)(B+1) becomes (ODD +1)(EVEN+1) = (EVEN)(ODD) = EVEN

case d: A is ODD and B is ODD
The expression (A+1)(B+1) becomes (ODD +1)(ODD+1) = (EVEN)(EVEN) = EVEN

Since we're told that (A+1)(B+1) is even, we can rule out case a.
So, cases b, c and d are all possible.

Now check the answer choices:
A. They are both even numbers. Case d says otherwise. ELIMINATE A
B. At least one of them is even. Case d says otherwise. ELIMINATE B
C. At least one of them is odd. Yes. All all 3 possible cases, at least one value is ODD

Answer: C
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