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A and B are integers. The expression (A+1)(B+1) is even. What can be
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05 Jul 2016, 12:21
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58% (01:05) correct 42% (01:10) wrong based on 207 sessions
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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
Re: A and B are integers. The expression (A+1)(B+1) is even. What can be
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05 Jul 2016, 13:20
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
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06 Jul 2016, 06:24
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
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16 Aug 2016, 16:28
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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
Re: A and B are integers. The expression (A+1)(B+1) is even. What can be
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06 Jan 2019, 01:39
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