What percent is x of y? (from a student)

[RonPurewal]

A student asked me the following question.

What percent is x of y?

(1) x = 3y

(2) x "” y = 6

Here the right answer is A and I got it right, however if I look at the explanation provided I don't understand why they plug in 3 and 4 respectively to x and y.

Quoted from the answer key:

To answer this question, we need to know the value of x/y. We can easily verify this by plugging in values of 3 and 4 for x and y, respectively. To answer the question "What percent is 3 of 4," we would simply take 3/4 and multiply it by 100.

[RonPurewal]

Interesting.

Well, it's clear that the numbers 3 and 4 have nothing to do with this problem, because they don't satisfy either statement (3 = 3*4 is not true, and neither is 3 - 4 = 6).

It seems they're just using those numbers to demonstrate that finding the ratio x/y is equivalent to finding x as a percentage of y. I think that's a strange way of doing it (and so I'll probably submit this problem for editing).
If you don't already know that percentages and ratios are correlated, you can set up the original question algebraically:

x = A% of y (where "A" stands for the "What" "” the answer to the problem)
x = (A/100)y
100x = Ay
100x/y = A

So, the question is exactly the same as asking "What is the value of 100x/y?"
Because the 100 is just a constant, you can solve for x/y and the result will be equivalent.

[RonPurewal]

By the way, note"”

If this were a multiple-choice question, you could NOT just find x/y; you'd actually have to find 100x/y, since that's the actual answer to the original question.

But, in data sufficiency, we're not concerned with the actual numerical value of the answer; we are only concerned with whether the answer can be found at all. So, being able to find x/y is exactly the same thing as being able to find 100x/y; it's clear that, if you have either one of these, you can find the other as well.