If the expression 4a-b is divisible by 4 for
any integer a and b, which of the following
MUST be true:
I. a is even
II. b is divisible by 4
III. b is positive
a. I only
b. II only
c. III only
d. I and II only
e. II and III only

Question

If the expression 4a-b is divisible by 4 for 
any integer a and b, which of the following 
MUST be true:
I. a is even
II. b is divisible by 4
III. b is positive
a. I only
b. II only 
c. III only
d. I and II only
e. II and III only

e.mccormick · Answer

Ummm.... hmmm... the question seems to be missing some restriction.  Like the word "even" as in "evenly dividable by 4" or the word "integer" as in "with an integer result."  Because without some added restriction, pretty much anything is dividable by 4.

e.mccormick · Answer

Ah...  OK.... I see....  I was overthinking it a bit.  The key is what I pointed out: anything is divisible by 4!

mary.rojas · Answer

.... i dont understand how to get the answer

e.mccormick · Answer

Well... Think about this.  Can -7 be divided by 4?

e.mccormick · Answer

So basically, is $-\dfrac{7}{4}$ a valid fraction?  If so, then odd things can be divided by 4 and negative things can be divided by 4....

e.mccormick · Answer

MUST be true: I. a is even II. b is divisible by 4 III. b is positive

I have to go, but think about this part this way:

Does it matter if something is even for it to be divided by 4?
Does it matter is something is dividable by 4 for it to be divided by 4?
Does it matter if something is negative for it to be divided by 4?

Anything that would not matter can be eliminated as a possible answer.

mary.rojas · Answer

thanks :)