SOLUTION: If y is an integer,which of the following is always an even integer? (a) y + 1 (b) 4y (c) 4y + 1 (d) .772

Question 393374: If y is an integer,which of the following is always an even integer?
(a) y + 1
(b) 4y
(c) 4y + 1
(d) .772
Found 2 solutions by neatmath, richard1234:
Answer by neatmath(302) (Show Source): You can put this solution on YOUR website!

The easiest way to do these types of problems, is to try to come up with examples that make the choices incorrect.

For example:

a) if I use 2, then 2+1=3 since 3 is not an even number, a must be wrong

c) again, if I use 2, then 4*2+1=9, which is not even! c must be wrong

d) .772 is obviously not an even number

The correct choice must be b!

No matter which choice of integer we use for y, 4y will always be even!

You may hear some arguments that 0 is NOT an even integer, but most, if not all, mathematicians consider 0 to be an even integer.

And for the sake of this question, they are obviously implying that 0 IS an even integer.

From mathforum.org:

"Integers are the whole numbers, negative whole numbers, and zero...
The terms even and odd only apply to integers; 2.5 is neither even nor
odd. Zero, on the other hand, is even since it is 2 times some
integer: it's 2 times 0."

I hope this helps!

Answer by richard1234(7193) (Show Source): You can put this solution on YOUR website!
If y = 0 (mod 2) then y + 1 = 0 + 1 = 1 (mod 2),

4y = 4(0) = 0 (mod 2)

4y + 1 = 4(0) + 1 = 1 (mod 2)

(d) makes no sense, it is already not an integer. Since (b) is the only integer 0 mod 2, it is the only number divisible by 2 and therefore, the only even integer.
RELATED QUESTIONS
if a is an integer, which of the following is always an odd integer? (a)4a+2 (b)10a... (answered by jim_thompson5910)
If a is an even integer and b is an odd integer, which of the following must be even?... (answered by mananth)
if k is a positive integer, which of the following must represent an even integer that is (answered by sudhanshu_kmr)
if x+3 is an even integer, then x could be which of the following? a) -2 b) -1 c)0... (answered by fcabanski)
if x and y are positive odd integer, where x>y which of the following is equal to x^2... (answered by Alan3354,josgarithmetic)
If q is an even integer, which of the expressions results in an even integer? (A)... (answered by Fombitz)
If x is an integer greater than 1 and if y = x + (1/x), which of the following (answered by jim_thompson5910)
If x+3 is an even integer, which of the following must be an even integer? (answered by Alan3354)
If the ratio of two positive integers is 3 to 2,which of the following statements about... (answered by Alan3354)