Hi ezzeldin.khaled79,
This question should be posted in the DS Sub-Forum here:
https://www.beatthegmat.com/data-sufficiency-f7.html
This question can be solved by TESTing VALUES.
We're asked if X is greater than 3. This is a YES/NO question.
1) X > 0
IF...
X = 1, then the answer to the question is NO.
X = 4, then the answer to the question is YES.
Fact 1 is INSUFFICIENT
2) root(X^3 - 9X + 4) > 2
IF...
X = -1, then the answer to the question is NO.
X = 4, then the answer to the question is YES.
Fact 2 is INSUFFICIENT
Combined, we know...
X > 0, meaning that X is POSITIVE
root(X^3 - 9X + 4) > 2
Since X has to be positive, we can find the 'lower limit' to what X could be....
IF...
X = 1, then root(X^3 - 9X + 4) = root(-4), which is NOT greater than 2, so X CANNOT be 1
X = 2, then root(X^3 - 9X + 4) = root(-6), which is NOT greater than 2, so X CANNOT be 2
X = 3, then root(X^3 - 9X + 4) = root(4), which is NOT greater than 2, so X CANNOT be 3.
From this work, we've proven that X cannot be 3 or less. As X increases from 3 though, the value becomes greater than root(4), so X MUST be greater than 3.
Combined, SUFFICIENT.
Final Answer:
C
GMAT assassins aren't born, they're made,
Rich
