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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.
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