Is x/(x+y) < 2

Okay, so first pass at this:

I thought about rephrasing the question, but since I don't know if x+y >0, I'm not sure I need to flip the sign or not. But a glance at the statements tells me that x+y will be positive in BOTH statements (since (>1)+(>1) > 2, and (>2) + (>0) > 2).

So I can rephrase:

x < 2x + 2y ?

-x < 2y?

In both of these statements the answer to this question must be 'yes,' since x and y are both positive in both statements, and a -(+) > 2(+) in all circumstances. (that is -x < 0 < 2y, since x and y are both positive).

Something about this didn't 'feel' like I'd done good work, or that I might have made a mistake somewhere (see my recent post about the important GMAT skill of self-reflection and certainty!) so I reflected a little bit more.

I figured in statement 1, x/(x+y) must be < 1. Since the denominator will be larger than the numerator. So it must also be <2.

Similar reasoning in statement 2. If you have a positive number in the numerator, and you add a positive number to that same number in the denominator, the numerator will be smaller, and so you'll end up with a positive fraction < 1, which is always < 2.

So D.
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Are you sure the source of the question is PowerPrep? That's a hard resource to even use these days, and the statements aren't written the way I'd expect official statements to be written. Regardless, using either statement, we know x and y are both positive, so x+y will certainly be greater than x, and since the numerator and denominator in x/(x+y) are both positive, x/(x+y) will thus be less than 1, so the answer is D.
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simplifying we get 1-y/ x+y

(1) x > 1, y > 1
for x=10 , y=2 it's less than 2 and all other values it's less than 2
Clearly insufficient

(2) x > 2, y > 0
for x=5 , y=10 the eqn is less than 2
Clearly sufficient

Therefore IMO A