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

Question

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

Bunuel · Answer

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.

Answer: C.

bhavinshah5685 · Answer

ans (C) 2n

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

fameatop · Answer

Answer C

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

dexerash · Answer

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

momentofzen · Answer

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.

akhilm · Answer

Answer: C
Any integer multiplied by an even number will always result in an Even integer.

momentofzen · Answer

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..."?

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

Bunuel · Answer

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.

momentofzen · Answer

Thank you! I did not realize 0 was considered an even number. Appreciate it. Cheers.

mcelroytutoring · Answer

Attached is a visual that should help.

JeffTargetTestPrep · Answer

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.

The answer is C.

Abhishek009 · Answer

Use the property of Even Numbers !!

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

So, Answer will be (C)

IF you want to check you can -

n = 2

2n = 4

If n = 3

2n = 6

Thus answer is (C)

kamranko · Answer

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

Bunuel · Answer

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

stonecold · Answer

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

Abhishek009 · Answer

Since, n is even , n = 2k

Thus, Only 2n = 4k 
  
Or, Answer will be (C) 2n

Shiv2016 · Answer

"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

nkmungila · Answer

any integer multiply by even number yields with Even integer,
here 2 is a even integer, hence it should be yield with Even number
hence answer should be 2n
Answer C

anshul1989 · Answer

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

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

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GMAT Problem Solving (PS) Questions

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

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