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Math Expert V
Joined: 02 Sep 2009
Posts: 53738
If x is odd, all EXCEPT which one of the following must be odd?  [#permalink]

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Difficulty:   35% (medium)

Question Stats: 73% (01:21) correct 27% (01:30) wrong based on 84 sessions

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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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Director  D
Joined: 18 Jul 2018
Posts: 754
Location: India
Concentration: Finance, Marketing
WE: Engineering (Energy and Utilities)
Re: If x is odd, all EXCEPT which one of the following must be odd?  [#permalink]

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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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Director  P
Status: Learning stage
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WE: Supply Chain Management (Energy and Utilities)
If x is odd, all EXCEPT which one of the following must be odd?  [#permalink]

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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) $$x^6 + 8x + 4$$

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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Senior Manager  P
Joined: 07 Jul 2012
Posts: 376
Location: India
Concentration: Finance, Accounting
GPA: 3.5
Re: If x is odd, all EXCEPT which one of the following must be odd?  [#permalink]

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Put x=1 in the answer choice. All the options give odd result except C.
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Manager  G
Joined: 07 Aug 2018
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GMAT 1: 560 Q39 V28 GMAT 2: 670 Q48 V34 If x is odd, all EXCEPT which one of the following must be odd?  [#permalink]

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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) $$x^6 + 8x + 4$$

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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Target Test Prep Representative P
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Re: If x is odd, all EXCEPT which one of the following must be odd?  [#permalink]

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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

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# Scott Woodbury-Stewart

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See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews Re: If x is odd, all EXCEPT which one of the following must be odd?   [#permalink] 19 Sep 2018, 18:05
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# If x is odd, all EXCEPT which one of the following must be odd?

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