SOLUTION: (a + b) / 2 is an integer,and b is even.Variable a MUST be: A) 0 B) 1 C) even D) odd E) a multiple of 3

Algebra.Com
Question 252670: (a + b) / 2 is an integer,and b is even.Variable a MUST be:
A) 0 B) 1 C) even D) odd E) a multiple of 3

Answer by palanisamy(496)   (Show Source): You can put this solution on YOUR website!
Given, (a + b) / 2 is an integer
(a+b)/2 = n , an integer
a+b = 2n, an even integer
a = 2n-b
Given b is even variable.
Therefore a is the difference of two even numbers and so it is even.

RELATED QUESTIONS

If a is an even integer and b is an odd integer, which of the following must be even?... (answered by mananth)
if (x+3)/2 is an integer, then x must be A. a negative integer B. a positive integer (answered by Edwin McCravy)
if k is a positive integer, which of the following must represent an even integer that is (answered by sudhanshu_kmr)
If the sum of n consecutive integers is 0, which of the following must be true? 1) n... (answered by scott8148)
a number is called " even - odd " if it is halfway between an even integer and an odd... (answered by Theo)
A number is called "even-odd" if it is halfway between an even integer and an odd... (answered by J2R2R)
The sum of seven consecutive positive integers is always (A) odd (B) a multiple of 7... (answered by solver91311)
1. Is q positive? (1) rs>0 and qs<0 (2) r>0 2. Is the positive integer p a multiple... (answered by edjones)
If the ratio of two positive integers is 3 to 2,which of the following statements about... (answered by Alan3354)