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# If n is an integer, is n even?

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If n is an integer, is n even?  [#permalink]

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10 Aug 2014, 11:22
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If n is an integer, is n even?

(1) 2n is divisible by 4
(2) n^2 is even

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Re: If n is an integer, is n even?  [#permalink]

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10 Aug 2014, 11:47
(1) $$2n$$ divisible by 4 means that n contains at least one 2 as a factor. Therefore the statement is sufficient.

(2)
odd*odd = odd
even*even = even

as $$n^2$$ is even, n must be even. Sufficient.

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Re: If n is an integer, is n even?  [#permalink]

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12 Aug 2014, 06:58
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If n is an integer, is n even?

(1) 2n is divisible by 4 --> 2n = 4k --> n = 2k = even. Sufficient.

(2) n^2 is even --> since n is an integer, then n^2 can be even only if n is even. Sufficient.

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Re: If n is an integer, is n even?  [#permalink]

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27 Jan 2015, 13:54
If n is an integer, is n even?

(1) 2n is divisible by 4
(2) n^2 is even

Hello Bunuel, I got confused when I was solving this question. First let's agree on a couple of points, 0 is an integer, 0 is neither even nor odd, & 0 is divisible by everything.

So when I look at the first statement it says 2n is divisible by 4, what if n=0, this statement would still be correct, however 0 is neither even nor odd, so how is statement one sufficient on it's own.

Regards,
YA
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Re: If n is an integer, is n even?  [#permalink]

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27 Jan 2015, 19:04
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Hi youssefhabouseif,

0 IS an EVEN integer, by definition. Here's why:

On a number line, consecutive integers fall into the pattern....even....odd.....even....odd.....even....odd....etc.

-2 = even
-1 = odd
0 = even
1 = odd
2 = even
Etc.

Knowing that 0 IS EVEN, you likely would have picked the correct answer, but it's important to keep this rule in mind - you'll likely use it on Test Day at least once.

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Re: If n is an integer, is n even?  [#permalink]

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28 Jan 2015, 00:47
1
youssefhabouseif wrote:
If n is an integer, is n even?

(1) 2n is divisible by 4
(2) n^2 is even

Hello Bunuel, I got confused when I was solving this question. First let's agree on a couple of points, 0 is an integer, 0 is neither even nor odd, & 0 is divisible by everything.

So when I look at the first statement it says 2n is divisible by 4, what if n=0, this statement would still be correct, however 0 is neither even nor odd, so how is statement one sufficient on it's own.

Regards,
YA

ZERO:

1. 0 is an integer.

2. 0 is an even integer. An even number is an integer that is "evenly divisible" by 2, i.e., divisible by 2 without a remainder and as zero is evenly divisible by 2 then it must be even.

3. 0 is neither positive nor negative integer (the only one of this kind).

4. 0 is divisible by EVERY integer except 0 itself.

Check more here: tips-and-hints-for-specific-quant-topics-with-examples-172096.html#p1371030
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Re: If n is an integer, is n even?  [#permalink]

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22 Aug 2016, 01:35
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Here given n is an integer we need to see if its even or odd
Statement 1 => 2n/4=Integer => N is divisible by 2 => Its even [[as The numbers that are divisible by 2 are evens ]]
Statement 2 => n^2=even => n must be even as POWER DOES NOT EFFECT THE EVEN OR ODD NATURE OF ANY NUMBER.
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Re: If n is an integer, is n even?  [#permalink]

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24 Sep 2018, 16:51
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Re: If n is an integer, is n even? &nbs [#permalink] 24 Sep 2018, 16:51
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