A and B are integers. The expression (A+1)(B+1) is even. What can be

Question

A and B are integers. The expression (A+1)(B+1) is even. What can be said about A and B?

A. They are both even numbers.
B. At least one of them is even.
C. At least one of them is odd.
D. They are both odd.
E. Nothing can be said surly on A and B

BrentGMATPrepNow · Accepted Answer

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

Nightfury14 · Answer

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
=========================================================================================
 "If a street performer makes you stop walking, you owe him a buck" 
"If this post helps you on your GMAT journey, drop a +1 Kudo "

Turkish · Answer

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

hsbinfy · Answer

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

Divyadisha · Answer

(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

Kimberly77 · Answer

Hi  BrentGMATPrepNow , I calculated as below and selected D. Not sure what's gone wrong?
(A+1)(B+1) = even

(A+1)= even
A = even - 1
A = odd

Same with B so they are both odd.

BrentGMATPrepNow · Answer

If we are told that (A+1)(B+1) = even, we can't then conclude that A+1 is even. 
All we can conclude is that EITHER A+1 is even OR B+1 is even (for they are both even)

For example, it could be the case that A = 2 and B = 3, in which case (A+1)(B+1) = (2+1)(3+1)= 12, which is even.
In this case, A is even

Kimberly77 · Answer

I see thanks  BrentGMATPrepNow .
To clarify if it have been (A+1)(B+1) = odd then can we conclude that A+1 = odd, A = odd - 1 = Even?
Thanks Brent

BrentGMATPrepNow · Answer

That's correct. 
In general: 
(ODD)(ODD) = ODD
(ODD)(EVEN) = EVEN
(EVEN)(ODD) = EVEN
(EVEN)(EVEN) = EVEN

So, if AB = ODD, then we can be certain that A and B are both ODD
If AB = EVEN, then all we can conclude is that at least one of the two values is EVEN.

Kimberly77 · Answer

Great explanation  BrentGMATPrepNow  and crystal clear now.

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

A and B are integers. The expression (A+1)(B+1) is even. What can be

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

A and B are integers. The expression (A+1)(B+1) is even. What can be

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards