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Bunuel
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BrentGMATPrepNow
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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.
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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
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Bunuel
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

(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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BrentGMATPrepNow
Bunuel
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

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

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.
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Kimberly77

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.

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
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BrentGMATPrepNow
Kimberly77

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.

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

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
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Kimberly77
BrentGMATPrepNow
Kimberly77

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.

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

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

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.
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Great explanation BrentGMATPrepNow and crystal clear now.
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