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

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

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New post 05 Jul 2016, 11:21
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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

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Re: A and B are integers. The expression (A+1)(B+1) is even. What can be  [#permalink]

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New post 05 Jul 2016, 12:20
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.

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Re: A and B are integers. The expression (A+1)(B+1) is even. What can be  [#permalink]

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New post 05 Jul 2016, 15:15
(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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Re: A and B are integers. The expression (A+1)(B+1) is even. What can be  [#permalink]

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New post 05 Jul 2016, 21:42
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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Re: A and B are integers. The expression (A+1)(B+1) is even. What can be  [#permalink]

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New post 06 Jul 2016, 05:24
Bunuel wrote:
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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Re: A and B are integers. The expression (A+1)(B+1) is even. What can be  [#permalink]

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New post 16 Aug 2016, 15:28
Top Contributor
Bunuel wrote:
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:

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Re: A and B are integers. The expression (A+1)(B+1) is even. What can be  [#permalink]

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Re: A and B are integers. The expression (A+1)(B+1) is even. What can be &nbs [#permalink] 06 Jan 2019, 00:39
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