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# Is a positive integer x odd? (1) 5x is odd. (2) (x + 5) is even.

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Math Expert
Joined: 02 Sep 2009
Posts: 56272
Is a positive integer x odd? (1) 5x is odd. (2) (x + 5) is even.  [#permalink]

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24 Sep 2018, 06:19
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Difficulty:

35% (medium)

Question Stats:

78% (00:34) correct 22% (00:45) wrong based on 29 sessions

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Is a positive integer x odd?

(1) 5x is odd.
(2) (x + 5) is even.

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Joined: 12 Sep 2015
Posts: 3848
Re: Is a positive integer x odd? (1) 5x is odd. (2) (x + 5) is even.  [#permalink]

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24 Sep 2018, 06:30
Top Contributor
Bunuel wrote:
Is a positive integer x odd?

(1) 5x is odd.
(2) (x + 5) is even.

Some important rules:
#1. ODD +/- ODD = EVEN
#2. ODD +/- EVEN = ODD
#3. EVEN +/- EVEN = EVEN

#4. (ODD)(ODD) = ODD
#5. (ODD)(EVEN) = EVEN
#6. (EVEN)(EVEN) = EVEN

Target question: Is a positive integer x odd?

Statement 1: 5x is odd.
5 is odd, so we have: (ODD)(x) is ODD
By rule #4, x must be ODD
So, the answer to the target question is YES, x IS odd
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: (x + 5) is even
5 is odd, so we have: (x + ODD) = EVEN
By rule #1, x must be ODD
So, the answer to the target question is YES, x IS odd
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Cheers,
Brent
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Re: Is a positive integer x odd? (1) 5x is odd. (2) (x + 5) is even.   [#permalink] 24 Sep 2018, 06:30
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