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# Is the integer n even? (1) n – 5 is an odd integer (2) n/5 is an even

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Is the integer n even? (1) n – 5 is an odd integer (2) n/5 is an even [#permalink]
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Orange08 wrote:
Is the integer n even?

(1) n – 5 is an odd integer.
(2) n/5 is an even integer.

Some important rules:
1. ODD - ODD = EVEN
2. EVEN - ODD = ODD
3. ODD - EVEN = ODD
4. EVEN - EVEN = EVEN

5. (ODD)(ODD) = ODD
6. (ODD)(EVEN) = EVEN
7. (EVEN)(EVEN) = EVEN

Target question: Is integer n even?

Statement 1: n – 5 is an odd integer
Since 5 is ODD, statement 1 is saying: n - ODD = ODD
From rule #2 above, we can conclude that n is EVEN
So, the answer to the target question is "YES, n IS even"
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: n/5 is an even integer.
First multiply both sides by 5 to get: n = (5)(some EVEN integer)
Since 5 is ODD, we statement 2 is saying: n = (ODD)(EVEN)
From rule #6 above, we can conclude that n is EVEN
So, the answer to the target question is "YES, n IS even"
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Cheers,
Brent

Originally posted by BrentGMATPrepNow on 21 Nov 2017, 10:25.
Last edited by BrentGMATPrepNow on 02 May 2020, 10:18, edited 1 time in total.
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Re: Is the integer n even? (1) n 5 is an odd integer (2) n/5 is an even [#permalink]
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Re: Is the integer n even? (1) n 5 is an odd integer (2) n/5 is an even [#permalink]
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