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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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Manager
Joined: 25 Jul 2010
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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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11 Sep 2010, 14:21
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Is the integer n even?

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

From 1, shouldn't the value of n be counted as 0?
n = 0, 2,4,6, etc.
Thus, can't tell if n is even for all values. 0 isn't considered even

From 2, n = 10, 20, 30 etc. and thus n is always even. sufficient.

Please correct me if I am wrong in my understanding for statement 1.
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Joined: 02 Sep 2009
Posts: 50623
Re: Is the integer n even? (1) n – 5 is an odd integer (2) n/5 is an even  [#permalink]

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11 Sep 2010, 14:28
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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.

From 1, shouldn't the value of n be counted as 0?
n = 0, 2,4,6, etc.
Thus, can't tell if n is even for all values. 0 isn't considered even

From 2, n = 10, 20, 30 etc. and thus n is always even. sufficient.

Please correct me if I am wrong in my understanding for statement 1.

Given: $$n=integer$$. Question: is $$n=even$$?

(1) $$n-5=odd$$ --> $$n-odd=odd$$ --> $$n=odd+odd=even$$. Sufficient.

(2) $$\frac{n}{5}=even$$ --> $$n=5*even=even$$. Sufficient.

P.S. Zero is an even number:

Zero is an even integer, though it's neither positive nor negative.

An even number is an integer that is "evenly divisible" by 2, i.e., divisible by 2 without a remainder.
An even number is an integer of the form $$n=2k$$, where $$k$$ is an integer.

So for $$k=0$$ --> $$n=2*0=0$$.

An odd number is an integer that is not evenly divisible by 2.
An odd number is an integer of the form $$n=2k+1$$, where $$k$$ is an integer.

Hope it helps.
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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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11 Sep 2010, 14:28
zero is a even number. any number that is multiple of 2 is even so 2* zero is zero.

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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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21 Nov 2017, 09:25
Top Contributor
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

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Re: Is the integer n even? (1) n – 5 is an odd integer (2) n/5 is an even &nbs [#permalink] 21 Nov 2017, 09:25
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