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

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Bunuel
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If x is an even number, which of the following must be odd? [#permalink] New post   19 Feb 2018, 23:09
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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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DavidTutorexamPAL
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If x is an even number, which of the following must be odd? [#permalink] New post   Updated on: 22 Feb 2018, 09:50
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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

(D) is our answer.

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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Re: If x is an even number, which of the following must be odd? [#permalink] New post   22 Feb 2018, 05:35
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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


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

Answer: D
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Re: If x is an even number, which of the following must be odd? [#permalink] New post   15 May 2020, 05:40
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


I. 3x + 1
x is even so 3*x will be even
And, any even no. +1 gives odd no.
therefore, In this expression the resulting no. will be odd


II. (5x)^2 + 2
x is even so 5*x will be even
And, Square of any even no. will be even
And, any even no. +2 gives an even no.
therefore, In this expression the resulting no. will be even


III. (x+1)^2
x is even so X+1 will be odd
And, square of any odd no. is odd
therefore, In this expression the resulting no. will be odd


So, in expressions I. and III. the resulting no. must be odd

Hence OA (D)
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Re: If x is an even number, which of the following must be odd? [#permalink] New post   15 May 2020, 08:36
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



BY USING PROPERTIES

(I) Odd*Even = Even & Even + Even = Odd
(II) (Odd*Even)^2 = Even , Even + Even = Even
(III) (Even + Odd)^2 = Odd

Answer must be (D)

PLUG IN AND CHECK

Let x = 2

I. \(3x + 1 = 3*2 + 1 = 7\)

II. \((5x)^2 + 2 = (5*2)^2 = 102\)

III. \((x + 1)^2 = (2+1)^2 = 9\)

Answer must be (D)
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Re: If x is an even number, which of the following must be odd? [#permalink]
15 May 2020, 08:36
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