Hi vincitygialam,
TESTing VALUES (or Picking Numbers; the Tactic can be referred to by a number of different 'titles') is one of the most useful Tactics for the Quant section (it can be used on far more than just the hard questions - up to 2/3 of the questions that you'll see in the Quant section can be beaten with this one approach). I've used that approach - along with Number Properties (which are essentially math rules that you can prove by TESTing VALUES) to solve the problem you posted.
We're told that U(U+V) is not equal to 0 and U > 0. We're asked if 1/(U+V) is less than the sum of 1/U and V. This is a YES/NO question. While it might look complex, it can be handled rather easily by TESTing VALUES and a bit of Number Property knowledge.
1) (U+V) > 0
IF....
U = 1, V = 1, then 1/(1+1) = 1/2 and 1/1 + 1 = 2... 1/2 IS less than 2 and the answer to the question is YES.
U = 1, V = 0, then 1/(1+0) = 1/1 and 1/1 + 0 = 1... 1 is NOT less than 1 and the answer to the question is NO.
Fact 1 is INSUFFICIENT.
2) V > 0
With the information in Fact 2, we know that BOTH U and V are POSITIVE. This allows us to use a particular Number Property rule to our advantage. Regardless of whether you are using positive fractions or positive integers, when BOTH variables are POSITIVE, 1/(U+V) will ALWAYS be LESS than 1/U.
As either (or both) of the values of U or V INCREASE, the value of 1/(U+V) will DECREASE. Obviously 1/U = 1/U, but when you 'add in' a positive value for V to that first fraction, the value of that fraction will DECREASE. Try any positive values for U and V and you'll see. Thus, 1/(U+V) will be LESS than 1/U. Adding V to 1/U simply increases the difference. Thus, the answer to the question is ALWAYS YES.
Fact 2 is SUFFICIENT.
Final Answer:
To properly master any Tactic (whether Quant or Verbal), you have to practice it repeatedly (first, with the easier prompts - then on tougher and tougher prompts so that you can hone that particular skill). Since you were likely never taught that Tactic in School, it might feel a little 'weird' at first. However, side-by-side, it's almost faster and easier than the traditional 'math' approaches that you might use. The Quant section of the GMAT is NOT a 'math test' - it's a 'critical thinking test' that requires lots of little calculations as you work through it. To maximize your performance in this section, you need to become more of a 'strategist' and less of a 'mathematician.'
GMAT assassins aren't born, they're made,
Rich