huongguyen wrote:
Is \(\frac{x}{x+y}\) < 2
(1) x > 1, y > 1
(2) x > 2, y > 0
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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REED ARNOLDManhattan Prep GMAT InstructorVideo: The 24 Things Every GMAT Studier Needs to DoThe Studying Verbal Starter Kit (...That's much more than a 'starter kit')The Studying Quant Starter Kit (...That's much more than a 'starter kit')The PERFECT data sufficiency question:On a three person bench, George sits in the middle of Alice and Darryl. If Alice is married, is an unmarried person sitting next to a married person?
1). George is married.
2). Darryl is not married.
Answer: