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If x is odd, all EXCEPT which one of the following must be odd?

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Bunuel
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If x is odd, all EXCEPT which one of the following must be odd? [#permalink] New post   31 Aug 2018, 00:01
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If x is odd, all EXCEPT which one of the following must be odd?

(A) \(x^2 + 4x + 6\)
(B) \(x^3 + 5x + 3\)
(C) \(x^4 + 6x + 7\)
(D) \(x^5 + 7x + 1\)
(E) \(x^6 + 8x + 4\)
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Re: If x is odd, all EXCEPT which one of the following must be odd? [#permalink] New post   31 Aug 2018, 00:15
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Since x is odd.

Lets take x = 1.

Only option C is even. Rest all are odd.

C is the answer

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If x is odd, all EXCEPT which one of the following must be odd? [#permalink] New post   31 Aug 2018, 00:48
Bunuel wrote:
If x is odd, all EXCEPT which one of the following must be odd?

(A) \(x^2 + 4x + 6\)
(B) \(x^3 + 5x + 3\)
(C) \(x^4 + 6x + 7\)
(D) \(x^5 + 7x + 1\)
(E) \(x^6 + 8x + 4\)


To find:-All EXCEPT which one of the following must be odd?
Implies that 4 incorrect answer options yield ODD output & one correct answer option yields EVEN output.

Three terms are there in each of the expressions in the answer options.

Note:-
1) An odd number in exponent form(\(Odd^{integer}\)) is always odd.
2) Multiplication of odd numbers always yield odd number.
3) Multiplication of odd numbers by even numbers always yield even number.
A. O+E+E=O
B. O+O+O=O
\(C. O+E+O=E\)
D. O+O+O=O
E. O+E+E=O

Ans. (C)
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Re: If x is odd, all EXCEPT which one of the following must be odd? [#permalink] New post   31 Aug 2018, 01:08
Put x=1 in the answer choice. All the options give odd result except C.
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If x is odd, all EXCEPT which one of the following must be odd? [#permalink] New post   18 Sep 2018, 06:29
Bunuel wrote:
If x is odd, all EXCEPT which one of the following must be odd?

(A) \(x^2 + 4x + 6\)
(B) \(x^3 + 5x + 3\)
(C) \(x^4 + 6x + 7\)
(D) \(x^5 + 7x + 1\)
(E) \(x^6 + 8x + 4\)


Another way to look at this problem is to regognize that x^n will always be odd in all options. In A and E booth other terms are even, so A and E booth result in an odd number. In B and D booth other terms are odd, so B and D will booth result in an odd number.

Only option C has an even and odd term, and will therefore result in an even number. Hence C is the answer.
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Re: If x is odd, all EXCEPT which one of the following must be odd? [#permalink] New post   19 Sep 2018, 18:05
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Bunuel wrote:
If x is odd, all EXCEPT which one of the following must be odd?

(A) \(x^2 + 4x + 6\)
(B) \(x^3 + 5x + 3\)
(C) \(x^4 + 6x + 7\)
(D) \(x^5 + 7x + 1\)
(E) \(x^6 + 8x + 4\)


Recall that even x odd = even and odd x odd = odd. Let’s analyze each choice.

A) x^2 + 4x + 6

odd + even + even = odd

B) x^3 + 5x + 3

odd + odd + odd = odd

C) x^4 + 6x + 7

odd + even + odd = even

Answer: C
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Re: If x is odd, all EXCEPT which one of the following must be odd? [#permalink] New post   14 Dec 2023, 05:48
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Re: If x is odd, all EXCEPT which one of the following must be odd? [#permalink]
14 Dec 2023, 05:48
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