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If x is a positive integer, which of the following must be odd? A. x+
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07 Jul 2021, 08:27
07 Jul 2021, 08:27
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If \(x\) is a positive integer, which of the following must be odd?
A. \(x+1\)
B. \(x^2+x\)
C. \(x^2+x+1\)
D. \(x^2−1\)
E. \(3x^2−3\)
A. \(x+1\)
B. \(x^2+x\)
C. \(x^2+x+1\)
D. \(x^2−1\)
E. \(3x^2−3\)
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Re: If x is a positive integer, which of the following must be odd? A. x+
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07 Jul 2021, 10:24
07 Jul 2021, 10:24
1
Carcass wrote:
If \(x\) is a positive integer, which of the following must be odd?
A. \(x+1\)
B. \(x^2+x\)
C. \(x^2+x+1\)
D. \(x^2−1\)
E. \(3x^2−3\)
A. \(x+1\)
B. \(x^2+x\)
C. \(x^2+x+1\)
D. \(x^2−1\)
E. \(3x^2−3\)
Let's test some values.
Try x = 1
A. 1 + 1 = 2 EVEN - ELIMINATE A
B. 1^2 + 1 = 2 EVEN - ELIMINATE B
C. 1^2 + 1 + 1 = 3 ODD - KEEP C
D. 1^2 − 1 = 0 EVEN - ELIMINATE D
E. 3(1^2) − 3 = 0 EVEN - ELIMINATE E
Answer: C
Cheers,
Brent
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Status:Founder & Quant Trainer
Affiliations: Prepster Education
Posts: 1546
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Location: India
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If x is a positive integer, which of the following must be odd? A. x+
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07 Jul 2021, 10:35
07 Jul 2021, 10:35
1
Carcass wrote:
If \(x\) is a positive integer, which of the following must be odd?
A. \(x+1\)
B. \(x^2+x\)
C. \(x^2+x+1\)
D. \(x^2−1\)
E. \(3x^2−3\)
A. \(x+1\)
B. \(x^2+x\)
C. \(x^2+x+1\)
D. \(x^2−1\)
E. \(3x^2−3\)
Remember:
(odd)(odd) = odd
(odd)(even) = even
(even)(odd) = even
(even)(even) = even
odd + odd = even
odd + even = odd
even + odd = odd
even + even = even
\(odd^{odd} = odd\)
\(odd^{even} = odd\)
\(even^{odd} = even\)
\(even^{even} = even\)
Now,
When \(x = odd\)
A. \(x+1 = odd + odd = even\)
B. \(x^2+x = odd^2 + odd = odd + odd = even\)
C. \(x^2+x+1 = odd^2 + odd + odd = odd + odd + odd = odd\)
D. \(x^2−1 = odd^2 - odd = odd - odd = even\)
E. \(3x^2−3 = 3odd^2 - odd = odd(odd) - odd = odd - odd = even\)
When \(x = even\)
A. \(x+1 = even + odd = odd\)
B. \(x^2+x = even^2 + even = even + even = even\)
C. \(x^2+x+1 = even^2 + even + odd = even + even + odd = odd\)
D. \(x^2−1 = even^2 - odd = even - odd = odd\)
E. \(3x^2−3 = 3even^2 - odd = odd(even) - odd = even - odd = odd\)
Hence, option C
