No, consider the following example:
If X=10, Y=3.
10/(2*3) leaves remainder 4. Great.
But 10/3 leaves remainder 1.
I really tried to do this algebraically, and then I broke down and plugged in. I think it's a great question, and I (personally) found it difficult to wrap my head around it without some numbers.
I tried a couple options for number 1. 24/10 and 24/5 gave the same remainder. Then I searched my head for a number that's divisible by something but not twice that something. I came up with 60/8 and 60/4.
I know this is a little sloppy, but when I laid out the algebra, I just couldn't see it.
For 2, I tried just one example and then it all made sense. Remainders are set up kind of like multiples. If I divide a number by 5 and get some remainder, then 5 more than that number will give me the same remainder. That's what number 2 is saying, and it was clear right away that it's sufficient.