hwiya320 wrote:If x and y are nonzero integers, what is the remainder when x is divided by y ?
(1) When x is divided by 2y, the remainder is 4.
(2) When x + y is divided by y, the remainder is 4.
Could someone please help me with solving this question efficiently?
Thanks
Pretty much all number property questions can be answered either by picking numbers or by understanding mathematical principles. This question is a great example of how sometimes a combination of methods is the most efficient approach.
Q: what's the remainder when x is divided by y?
(1) x/2y = nrem4, where n is an integer.
Well, from x/2y we can't get x/y plus an integer, so it's unlikely that this will be sufficient. Let's pick numbers to see if we can get more than 1 answer to the original question.
We can pick x=10 and y=3 (because 10/6 = 1rem4).
When we divide x by y, we get 10/3 = 3rem1.
We can pick x=12 and y=4 (because 12/8 = 1rem4).
When we divide x by y, we get 12/4 = 3rem0.
We got two different remainders: insufficient.
(2) (x+y)/y = nrem4.
This one we can simplify and, if we understand the rules, don't need to pick numbers.
(x+y)/y = x/y + y/y
Well, we know that y/y has no remainder at all. So, if "x/y + y/y" has a remainder of 4, the entire remainder must come from the "x/y" portion.
Therefore, the remainder when x is divided by y is 4: sufficient.
(2) is suff, (1) is not: choose (B).
