My guess is that something that can save you time on questions like this is to say to yourself:
"Any time I see algebraic fractions with different denominators, I am going to put them over a common denominator."
It's almost always helpful, and it's usually necessary.
If you did this, but then weren't sure if the combined statements were sufficient, then consider the following about systems of equations in which one equation is XY = ? and the other is X+Y = ?:
1. In these systems, there are usually 2 solutions, and X can be either one as long as Y is the other one.
2. You can often guess what the numbers are by looking at the equations. In this case, it's not unreasonable to say that you could guess that the two numbers are 4 and 12.
3. Once you know that EITHER x = 12, y = 4 OR x = 4, y = 12, you can plug both sets of values into the prompt and see what happens. In this case, different outcomes. In other cases, they could be the same.
4. If all else fails, you can use substitution to set up a quadratic equation and find the two values that way. Here, x = 16 - y, so you can substitute to get (16 - y)*y = 48 and solve the resulting quadratic equation. This is messy though. Ty to guess at the two numbers first.
Hope this helps. Let me know if the time sink was something totally different.[/url]
Greg Michnikov, Founder of GMAT Boost
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