If positive integer 36y is divisible by 10, which of the following mus

HI shasadou,

Although the prompt doesn't state it, I think that it is supposed to state that "Y is an INTEGER."

Given that, we can use Prime Factorization to deal with this prompt.

Again, assuming that Y is an integer, we're told that 36Y is divisible by 10. This means that 36Y must have a "2" and a "5" among its prime factors.

36 = (2)(2)(3)(3), so it has the '2' that we're looking for, but it doesn't have the '5.' This means that the Y must contain at least a "5" (although it could have other prime factors also, including additional 5s). This is all meant to say that Y MUST be a multiple of 5. Since the prompt asks for what MUST be true, we can use Y=5 to assess the Roman Numerals.

I. Y^2 is divisible by 25

Y=5
Y^2 = 25, which IS divisible by 25
Any larger multiple of 5 will also be divisible by 25.
Roman Numeral 1 is always true.
Eliminate Answers B and C.

II. Y^2 is divisible by 100

With the work that we did in Roman Numeral 1, we've proven that this is NOT always true.
Eliminate Answer D.

III. 3Y/15 is an integer

Even before we consider the value of Y, we can simplify this fraction....
3Y/ 15 = Y/5

So, is Y/5 always an integer? We already proved that Y had to be a multiple of 5, so this Roman Numeral is also always true.
Eliminate Answer A.
If we had dealt with this Roman Numeral immediately after dealing with Roman Numeral 1, then we wouldn't even have had to deal with Roman Numeral 2. There's only one answer that includes Roman Numerals 1 and 3...

Final Answer:

GMAT assassins aren't born, they're made,
Rich