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If x is an odd integer, which of the following is also an odd integer?

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Bunuel
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If x is an odd integer, which of the following is also an odd integer? [#permalink] New post  15 Oct 2019, 06:37
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A
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C
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E

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If x is an odd integer, which of the following is also an odd integer?

(A) 2x
(B) 4x + 2
(C) x^2 + 3
(D) x^2 + x + 3
(E) x^2 + 2x + 1
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Re: If x is an odd integer, which of the following is also an odd integer? [#permalink] New post  15 Oct 2019, 06:51
Bunuel wrote:
If x is an odd integer, which of the following is also an odd integer?

(A) 2x
(B) 4x + 2
(C) x^2 + 3
(D) x^2 + x + 3
(E) x^2 + 2x + 1


Substitution Method:

Let x = 1

(A) 2x --> 2 --> Even
(B) 4x + 2 --> 4*1 + 2 = 6 --> Even
(C) x^2 + 3 --> 1^2 + 3 = 4 --> Even
(D) x^2 + x + 3 --> 1^1 + 1 + 3 = 5 --> Odd
(E) x^2 + 2x + 1 --> 1^2 + 2*1 + 1 = 4 --> Even

IMO Option D
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Re: If x is an odd integer, which of the following is also an odd integer? [#permalink] New post  15 Oct 2019, 08:05
Bunuel wrote:
If x is an odd integer, which of the following is also an odd integer?

(A) 2x
(B) 4x + 2
(C) x^2 + 3
(D) x^2 + x + 3
(E) x^2 + 2x + 1


(A) 2*Odd = Even , Even + Even = Even
(B) 4*Odd = Even , Even + Even = Even
(C) Odd^2 = Odd , Odd + Odd = Even
(D) Odd^2 = Odd , Odd + Odd = Even , Even + Odd = Odd
(E) Odd^2 = Odd , 2*Odd = Even , Odd + Even = Odd , Odd + 1 = Even

Hencem Answer must be (D)
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If x is an odd integer, which of the following is also an odd integer? [#permalink] New post  15 Oct 2019, 20:27
x=odd
even*anything = even--> A is incorrect
Even*odd + even = even + even = even--> B is out
odd+odd = even -->C is out
odd+odd =even +odd = odd -->D is correct
odd+even = odd + odd = even -->E is out


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If x is an odd integer, which of the following is also an odd integer? [#permalink]
15 Oct 2019, 20:27
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