This question is quirky in that it tests you on math rules and patterns that you probably know, but in ways that you're not used to thinking about...
We're told that neither X nor Y are equal to 0. We're also told that (X^2)(Y^2) - XY = 6. We're asked which of the following COULD be the value of Y in terms of X...
The first interesting thing about this question is the use of the word COULD....that word implies that there's MORE THAN ONE possible solution.
The second interesting thing is that the 'term' (XY) can be factored out of the 'left side' of the equation. Normally, you look to factor our a single variable or number, but here, it's the product of two variables that you can factor out. Doing so gives us...
XY(XY - 1) = 6
While this looks complicated, there's an easy pattern here:
(number)(number - 1) = 6
Can you think of 2 numbers, that differ by 1, that you can multiply to get 6?
You should be thinking 2 and 3... because (3)(3-1) = 6
So XY = 3 is a possible solution. In this case, Y = 3/X. The wording of the prompt makes me think that there should be another solution though, so is there ANOTHER pair of numbers, that differ by 1, that you can multiply together to get 6? Hint: the numbers do NOT have to be positive....
How about -2 and -3....
(-2)(-2-1) = 6
So XY = -2 is another possible solution. In this case, Y = -2/X
There's only one answer that includes both of those solutions...
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