Question

A number is called "even-odd" if it is halfway between n even integer and an odd integer. If x is an even-odd number. Which of the following must be true?
a) 2x is an integer
b) 2x is even-odd
c) x is halfway between two even integers

Answer 1

Here's your 'even-odd' numbers, \(\dfrac{2k + (2j+1)}{2}\), where j and k are integers.

Now what?

Answer 2

2x will always be odd

Answer 3

\[\frac{2k+2j+1}{2}=x\\2x=2(k+j)+1\]

Answer 4

i wrote the question wrong

Answer 5

A number is called "even-odd" if it is halfway between an even integer and an odd integer. If x is an even-odd number. Which of the following must be true?
a) 2x is an integer
b) 2x is even-odd
c) x is halfway between two even integers

Answer 6

the answer is a

Answer 7

and in particular, an odd integer

Answer 8

ok