SOLUTION: 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 ? I 2x is an inte

Question 363479: 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 ?
I 2x is an integer
II 2x is even-odd
III x is halfway between two even integers

(A) I only
(B) II only
(c) I and II only
(D) II and III only
(E) I, II, and III

Answer by J2R2R(94) (Show Source): You can put this solution on YOUR website!
Let us say the two numbers are 2m + 1 (odd) and 2n (even) where m and n are integers irrespective of being odd or even.

Halfway between them is (2m + 1 + 2n)/2 = (m + n) + �

So the even-odd number X must be of the form N + � where N can be any integer.

Therefore
2X is an integer (odd)
2X cannot be an even-odd number since 2X is an integer and not of the form N + �
X cannot be halfway between two even integers since half way between two even integers is an integer too and X is of the form N + �

Therefore only the first one is correct which means the answer is A.
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