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A and B are integers. The expression (A+1)(B+1) is even. What can be s
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07 Jul 2021, 08:29
07 Jul 2021, 08:29
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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
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 s
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07 Jul 2021, 10:25
07 Jul 2021, 10:25
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Carcass 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. 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
One 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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Re: A and B are integers. The expression (A+1)(B+1) is even. What can be s
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07 Jul 2021, 10:39
07 Jul 2021, 10:39
1
Carcass 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. 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
Remember:
(odd)(even) = even
(even)(odd) = even
(even)(even) = even
Case I:
(odd)(even) = even
(A + 1)(B + 1) = even
i.e. A = even, B = odd
Case II:
(even)(odd) = even
(A + 1)(B + 1) = even
i.e. A = odd, B = even
Case III:
(even)(even) = even
(A + 1)(B + 1) = even
i.e. A = odd, B = odd
We can see, one of them has to be odd
Hence, option C
