Which of the follwing must be an even integer

[Marisa]

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

a) n + 1
b) n + 2
c) n^2 + 2
d) n^2 + n
e) n^2 + 2n

I used an odd and even number as examples and got different answers. Can anyone explain? Thank you in advance!

[Uri]

any odd integer, when squared, will produce another odd integer. and two odd integers, when added, will produce an even integer. thus (D) is satisfied for odd inetegers.

now...any even integer, when squared, will produce an even integer. and two even integers, when added, will produce another even integer. so, (D) is satisfied in this case also.

hence, (D) is the answer.

[x2suresh]

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

a) n + 1
b) n + 2
c) n^2 + 2
d) n^2 + n
e) n^2 + 2n

I used an odd and even number as examples and got different answers. Can anyone explain? Thank you in advance!

n^2+n = n(n+1)

if n is odd n+1 even
odd*even = even
if n is even n+1 odd
even*odd = even

D