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Math Expert V
Joined: 02 Sep 2009
Posts: 60647
If n is an integer, which of the following must be even?  [#permalink]

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9 00:00

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Question Stats: 97% (00:24) correct 3% (00:28) wrong based on 1946 sessions

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If n is an integer, which of the following must be even?

(A) n+1
(B) n+2
(C) 2n
(D) 2n +1
(E) n^2

Practice Questions
Question: 44
Page: 158
Difficulty: 550

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Math Expert V
Joined: 02 Sep 2009
Posts: 60647
Re: If n is an integer, which of the following must be even?  [#permalink]

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SOLUTION

If n is an integer, which of the following must be even?

(A) n+1
(B) n+2
(C) 2n
(D) 2n +1
(E) n^2

ANY integer multiplied by even number yields even result, thus option C must be even.

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Re: If n is an integer, which of the following must be even?  [#permalink]

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1
1
ans (C) 2n

n=1 => 2n = 2 =>even
n=2 => 2n = 4 => even
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Re: If n is an integer, which of the following must be even?  [#permalink]

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1

Any integer multiplied by an even number will always yield Even integer.
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Re: If n is an integer, which of the following must be even?  [#permalink]

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2
Bunuel wrote:

If n is an integer, which of the following must be even?

(A) n+1
(B) n+2
(C) 2n
(D) 2n +1
(E) n^2

Since n is an integer, it can be EVEN or ODD.
But any integer when multiplied by 2 is even.
For example, 3 * 2 = 6 (even)
The rule is: EVEN * ODD = EVEN
EVEN * EVEN = EVEN
ODD * ODD = ODD

A) we cant say as it depends if n is odd or even
B) same as A)
C) Even as n is multiplied by 2
D) It is ODD as EVEN+1 = ODD
E) depends if n is even or odd.

Hence C
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Re: If n is an integer, which of the following must be even?  [#permalink]

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I thought that an integer could be 0. If that is the case, then 2*(0), would equal 0, which is not equal an even number. Thus, it does not answer the question. Can someone please clarify? Thanks.
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Re: If n is an integer, which of the following must be even?  [#permalink]

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Any integer multiplied by an even number will always result in an Even integer.
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Re: If n is an integer, which of the following must be even?  [#permalink]

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Can you please clarify. My understanding is that 0 is an integer. If that the case you cant say any integer multiplied by an even number equals an even number. Because 0 multiplied by an even number equals 0, which is not an even number.

Im wondering if this question is erroneous. Shouldnt the question state any "if n is a positive or negative integer..."?
Math Expert V
Joined: 02 Sep 2009
Posts: 60647
Re: If n is an integer, which of the following must be even?  [#permalink]

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momentofzen wrote:
Can you please clarify. My understanding is that 0 is an integer. If that the case you cant say any integer multiplied by an even number equals an even number. Because 0 multiplied by an even number equals 0, which is not an even number.

Im wondering if this question is erroneous. Shouldnt the question state any "if n is a positive or negative integer..."?

Zero is an even integer. Zero is nether positive nor negative, but zero is definitely an even number.

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 (in fact zero is divisible by every integer except zero itself).

I think you should brush-up fundamentals on Number Theory: math-number-theory-88376.html

All DS Number Properties Problems to practice: search.php?search_id=tag&tag_id=38
All PS Number Properties Problems to practice: search.php?search_id=tag&tag_id=59

Hope it helps.
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Re: If n is an integer, which of the following must be even?  [#permalink]

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1
Thank you! I did not realize 0 was considered an even number. Appreciate it. Cheers.
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Re: If n is an integer, which of the following must be even?  [#permalink]

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Attached is a visual that should help.
Attachments Screen Shot 2016-05-10 at 5.49.39 PM.png [ 53.73 KiB | Viewed 39744 times ]

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Re: If n is an integer, which of the following must be even?  [#permalink]

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Bunuel wrote:
If n is an integer, which of the following must be even?

(A) n+1
(B) n+2
(C) 2n
(D) 2n +1
(E) n^2

To solve this question, we need to consider a few odd/even rules.

1) (even + even) or (odd + odd) = even

2) even + odd = odd

3) (even x even) or (even x odd) = even (Note that an even integer times any integer, whether even or odd, will yield an even answer for the product.)

4) odd x odd = odd

Doing a quick scan of our answer choices allows us to select C as the correct option. Regardless whether n is even or odd, 2 (which is even) times any integer will always be even.

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Re: If n is an integer, which of the following must be even?  [#permalink]

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Bunuel wrote:
If n is an integer, which of the following must be even?

(A) n+1
(B) n+2
(C) 2n
(D) 2n +1
(E) n^2

Practice Questions
Question: 44
Page: 158
Difficulty: 550

Use the property of Even Numbers !!

A number is even if it is divisible by 2, among the options given only (C) matches...

IF you want to check you can -

n = 2

2n = 4

If n = 3

2n = 6

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Re: If n is an integer, which of the following must be even?  [#permalink]

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Bunuel wrote:
If n is an integer, which of the following must be even?

(A) n+1
(B) n+2
(C) 2n
(D) 2n +1
(E) n^2

Practice Questions
Question: 44
Page: 158
Difficulty: 550

I think you forgot about zero  In one of the prep author considered "0" neither even nor odd. if we consider "0", which I assume is not, as an even number it would be C
Math Expert V
Joined: 02 Sep 2009
Posts: 60647
Re: If n is an integer, which of the following must be even?  [#permalink]

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kamranko wrote:
Bunuel wrote:
If n is an integer, which of the following must be even?

(A) n+1
(B) n+2
(C) 2n
(D) 2n +1
(E) n^2

Practice Questions
Question: 44
Page: 158
Difficulty: 550

I think you forgot about zero  In one of the prep author considered "0" neither even nor odd. if we consider "0", which I assume is not, as an even number it would be C

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: number-properties-tips-and-hints-174996.html
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GRE 1: Q169 V154 If n is an integer, which of the following must be even?  [#permalink]

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Here as n is an integer -> n can be even or odd
Notice that 2n is always even

Hence C
Additionally 2n+1 is always odd and n and n^2 will have same even/odd nature

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Re: If n is an integer, which of the following must be even?  [#permalink]

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Bunuel wrote:
If n is an integer, which of the following must be even?

(A) n+1
(B) n+2
(C) 2n
(D) 2n +1
(E) n^2

Since, n is even , n = 2k

Thus, Only 2n = 4k

Or, Answer will be (C) 2n

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Re: If n is an integer, which of the following must be even?  [#permalink]

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"MUST BE": Condition is always true in all the possible cases.

A number multiplied by 2 is always even. Thus the answer is 2n.

If n is odd (e.g. 3), 2n=2*3=6
If n is even (e.g. 2), 2n=2*2=4
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Re: If n is an integer, which of the following must be even?  [#permalink]

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any integer multiply by even number yields with Even integer,
here 2 is a even integer, hence it should be yield with Even number
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Re: If n is an integer, which of the following must be even?  [#permalink]

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1
Any integer multiplied by an even number will always yield Even integer.

n=1 => 2n = 2 =>even
n=2 => 2n = 4 => even

hence, correct option is C Re: If n is an integer, which of the following must be even?   [#permalink] 27 Jan 2018, 07:07

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