For #2 - I'm a bit confused why statement 2 is sufficient when you have two possibles. X could be negative or positive and then it would keep the sign because it's cubed. Or am I thinking about this incorrectly?
Good question! It's easy to get turned around here. Remember that the statement acts as a rule we have to follow, so Statement 2 is asking us to consider what happens if x-cubed is definitely negative. The only way to get a negative number by cubing it is to start with a negative number (as you said, because it keeps the sign). Positive numbers would keep the sign when cubed, but they'd be invalid, because they don't follow the rule from Statement 2 that x-cubed is negative.
For Question 2, Is x< 0 ?. Statement 1. -2x>0. The statement says the -2x is greater than 0. This is only possible, if x is negative. In that case, without solving further, can we conclude, x is negative and thus less than zero. ?
Hi! If you're looking for harder material, check out our Challenge Problem Archive here: www.manhattanprep.com/gmat/store/online-resources/gmat-challenge-problem-archive/
Very very nicely explained
@12:50
For #2 - I'm a bit confused why statement 2 is sufficient when you have two possibles. X could be negative or positive and then it would keep the sign because it's cubed. Or am I thinking about this incorrectly?
Good question! It's easy to get turned around here. Remember that the statement acts as a rule we have to follow, so Statement 2 is asking us to consider what happens if x-cubed is definitely negative. The only way to get a negative number by cubing it is to start with a negative number (as you said, because it keeps the sign). Positive numbers would keep the sign when cubed, but they'd be invalid, because they don't follow the rule from Statement 2 that x-cubed is negative.
For Question 2, Is x< 0 ?.
Statement 1. -2x>0. The statement says the -2x is greater than 0. This is only possible, if x is negative. In that case, without solving further, can we conclude, x is negative and thus less than zero. ?
Yes! Great alternative way of thinking about it.
for the second questions, what if x equals 0?
If x = 0, that would constitute a "no" answer to the question.
There could be harder questions :/
Hi! If you're looking for harder material, check out our Challenge Problem Archive here: www.manhattanprep.com/gmat/store/online-resources/gmat-challenge-problem-archive/
@@manhattanprepgmat6791 thanks!