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Now let us take it down fat and very fast, cos this is a very wussy question where we have to save time for the other tough problems we should not take more than 10 seconds to solve it . 9x>10x implies x < 0 9 (Awesome ) x+3 > 0 implies x > -3 ( not good ) Answer is A

9x>10X only if x is -ve it cant be greater when x is + ve hence 1 is sufficient but statement 2 is insufficient as x can hav the value as 0 and any + ve num zero is neither +ve nor - ve hence insufficient A is the answer

(1) 9x > 10x --> rearrange: \(0>10x-9x\) --> \(0>x.\) Sufficient. (2) x + 3 is positive --> \(x+3>0\) --> \(x>-3\). Not sufficient.

Answer: A.

Hi Bunuel.

What is unclear for me is not the probelm by itself (I picked the right answer but the first statement

1) 0 > of something then X must be negative. The answer is definitevely YES.

Instead, I have obtained YES too but X is definetevely positive. In this scenario is the same, the most imprtant thing is to have a definitive answer, or is wrong thinking in this way??

(1) 9x > 10x --> rearrange: \(0>10x-9x\) --> \(0>x.\) Sufficient. (2) x + 3 is positive --> \(x+3>0\) --> \(x>-3\). Not sufficient.

Answer: A.

Hi Bunuel.

What is unclear for me is not the probelm by itself (I picked the right answer but the first statement

1) 0 > of something then X must be negative. The answer is definitevely YES.

Instead, I have obtained YES too but X is definetevely positive. In this scenario is the same, the most imprtant thing is to have a definitive answer, or is wrong thinking in this way??

Thanks

Well, from (1) we have that x<0, so x is negative not positive.

As for your question: in a Yes/No Data Sufficiency question, statement(s) is sufficient if the answer is “always yes” or “always no” while a statement(s) is insufficient if the answer is "sometimes yes" and "sometimes no".

Fact 1 tells us that 9X > 10X. That is a specific "restriction" that eliminates certain possible values of X.

ANY POSITIVE value for X (even a positive fraction), won't "fit" with that inequality. Neither will the value 0.

IF....X = 1/3 9(1/3) = 3 10(1/3) = 3.3333 3 is NOT > than 3.3333, so X CANNOT be 1/3.

9(0) is NOT > than 10(0), so X CANNOT be 0.

You can also do algebra to simplify the inequality....

9X > 10X -9X -9X 0 > X

In either approach, you can prove that X CANNOT be positive and CANNOT be 0. Negative values are all that are left, so the answer to the question is ALWAYS YES. Fact 1 is SUFFICIENT.

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