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# If x is an even number, which of the following must be odd?

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Math Expert
Joined: 02 Sep 2009
Posts: 58434
If x is an even number, which of the following must be odd?  [#permalink]

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19 Feb 2018, 23:09
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Difficulty:

25% (medium)

Question Stats:

73% (01:01) correct 27% (00:53) wrong based on 85 sessions

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If x is an even number, which of the following must be odd?

I. 3x + 1

II. (5x)^2 + 2

III. (x + 1)^2

(A) I only

(B) III only

(C) I and II only

(D) I and III only

(E) I, II, and III

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examPAL Representative
Joined: 07 Dec 2017
Posts: 1153
If x is an even number, which of the following must be odd?  [#permalink]

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Updated on: 22 Feb 2018, 09:50
1
Bunuel wrote:
If x is an even number, which of the following must be odd?

I. 3x + 1

II. (5x)^2 + 2

III. (x + 1)^2

(A) I only

(B) III only

(C) I and II only

(D) I and III only

(E) I, II, and III

Even/Odd questions are usually solvable without explicit calculations, using basic properties.
We'll look for such an answer, a Logical approach.

I. x is even --> 3x is odd*even=even --> 3x+1 is even + odd= odd
II. x is even --> 5x is odd*even=even --> (5x)^2 is even*even=even --> (5x)^2 + 2 is even+even=even
III. x is even --> x+1 is even+odd=odd --> (x+1)^2 is odd*odd=odd

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Originally posted by DavidTutorexamPAL on 20 Feb 2018, 00:08.
Last edited by DavidTutorexamPAL on 22 Feb 2018, 09:50, edited 1 time in total.
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Joined: 18 Jul 2017
Posts: 57
Re: If x is an even number, which of the following must be odd?  [#permalink]

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22 Feb 2018, 05:35
1
If x is an even number, which of the following must be odd?

I. 3x + 1

II. (5x)^2 + 2

III. (x + 1)^2

(A) I only

(B) III only

(C) I and II only

(D) I and III only

(E) I, II, and III

Lets substitute x=2,
1) 3(2) + 1 = 7 (ODD)
2) (5(2))^2 + 2 = 102 (Even)
3) (2+1)^2 = 9 (ODD)

So the option id D
Target Test Prep Representative
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2815
Re: If x is an even number, which of the following must be odd?  [#permalink]

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22 Feb 2018, 09:23
Bunuel wrote:
If x is an even number, which of the following must be odd?

I. 3x + 1

II. (5x)^2 + 2

III. (x + 1)^2

(A) I only

(B) III only

(C) I and II only

(D) I and III only

(E) I, II, and III

We may recall that even + odd = odd and odd + even = odd.

I. 3x + 1

Since x is even, 3*(even) + 1 = even + odd = odd.

I is true.

II. (5x)^2 + 2

(5*(even))^2 + 2 = even + even = even

II is not true.

III. (x + 1)^2

(even + 1)^2 = (odd)^2 = odd

III is true.

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Re: If x is an even number, which of the following must be odd?   [#permalink] 22 Feb 2018, 09:23
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