Data Sufficiency

Is x<0?

1. x^3 < x^4

2. x^3<x^5

I don't understand why the answer is E

Thanks,

1) x^4 - x^3 > 0
i.e. x^3 (x-1) >0

The above will be true if bot x^3 >0 and x-1>0 or x^3 < 0 and x-1 <0
Two answers ....Insuff

2) x^5 - x^3 > 0
x^3 (x-1) (x+1) >0
using same concept above, Again multiple answers and hence insuff.

Combining, we cannot get unique answer


Hence E

schumi_gmat wrote:1) x^4 - x^3 > 0
i.e. x^3 (x-1) >0

The above will be true if bot x^3 >0 and x-1>0 or x^3 < 0 and x-1 <0
Two answers ....Insuff

2) x^5 - x^3 > 0
x^3 (x-1) (x+1) >0
using same concept above, Again multiple answers and hence insuff.

Combining, we cannot get unique answer


Hence E

Can we really work like this with inequalities?

X<1 then can we say X-1<0?

There is nothing wrong in subtracting values on both sides

Be careful when you cross multiply or Divide.

IMO B

2) x^3 < x^5

This is only true for x>1 ....we can test other values

x = fraction ....this won't be true for fractions so discard

x = negative integers ....wont be true either so the only way this can be true is x > 1


I disagree with the OA = E ....unless someone can give a counter example to prove this is not sufficient.

neoreaves wrote:IMO B

2) x^3 < x^5

This is only true for x>1 ....we can test other values

x = fraction ....this won't be true for fractions so discard

x = negative integers ....wont be true either so the only way this can be true is x > 1


I disagree with the OA = E ....unless someone can give a counter example to prove this is not sufficient.

Bro..

But again going by ur wrds that X >1, then u shuld have opted D. Still it is WRONG!!

here is the catch!

Did u try for X =0.5,0.25 etc??

Logic shall fail!!

gmatmachoman wrote:

neoreaves wrote:IMO B

2) x^3 < x^5

This is only true for x>1 ....we can test other values

x = fraction ....this won't be true for fractions so discard

x = negative integers ....wont be true either so the only way this can be true is x > 1


I disagree with the OA = E ....unless someone can give a counter example to prove this is not sufficient.

Bro..

But again going by ur wrds that X >1, then u shuld have opted D. Still it is WRONG!!

here is the catch!

Did u try for X =0.5,0.25 etc??

Logic shall fail!!

ok i see your point ...though your example of x = 0.5 or 0.25 wont work ....

but x = -0.5 will ...so yeah it should be E

neoreaves wrote:

gmatmachoman wrote:

neoreaves wrote:IMO B

2) x^3 < x^5

This is only true for x>1 ....we can test other values

x = fraction ....this won't be true for fractions so discard

x = negative integers ....wont be true either so the only way this can be true is x > 1


I disagree with the OA = E ....unless someone can give a counter example to prove this is not sufficient.

Bro..

But again going by ur wrds that X >1, then u shuld have opted D. Still it is WRONG!!

here is the catch!

Did u try for X =0.5,0.25 etc??

Logic shall fail!!

ok i see your point ...though your example of x = 0.5 or 0.25 wont work ....

but x = -0.5 will ...so yeah it should be E

hahahhaa..nice catch...Yeah it should have been x=-0.5,-0.25...Seems sunday midnite blues has struck me!