Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized for You

we will pick new questions that match your level based on your Timer History

Track Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

I don't think its legal to multiply by x^3 in an inequality.

I think MA you have done that in arriving at your solution.

Because you don't know if the sign will change or not. I am concluding this from the thread on number properties:

"x>1/x
Again you CAN'T multiply both sides by x because you don't know if x is positive or negative. What you have to do is to move the right side to the left:
x-1/x>0
"

I'd add another question: how could you multiply the 2 members of the inequality by x^4 if x could be = 0?

I solved this way:
1/x^3-1/x^2 <= 0
1/x^2(1/x-1)<=0
since 1/x^2 is always positive, the sign is determined by 1/x-1
so 1/x<=1 => x>=1 (I lost the "x<0" solution)
Where is the mistake?

I'd add another question: how could you multiply the 2 members of the inequality by x^4 if x could be = 0?

I solved this way: 1/x^3-1/x^2 <= 0 1/x^2(1/x-1)<=0 since 1/x^2 is always positive, the sign is determined by 1/x-1 so 1/x<=1 => x>=1 (I lost the "x<0" solution) Where is the mistake?

x can't be = 0....as we have terms in 1/x, which will make 1/x = infinity...in ur soln, everything is correct except when u reverse
1/x <= 1....u can't just say x > = 1....consider when x < 0, that also satisfies 1/x <= 1