Is x

Question

Is x < 0 ?

(1) x^3 < x^2
(2) x^3 < x^4

gmat1220 · Answer

1) Insufficient. x < 0 or 0< x < 1
2) Insufficient. x < 0 or x > 1

1) + 2) Sufficient.

if 0 < x < 1 then x^4 < x^3 < x^2
if x < 0 then x^3 is negative and x^2 and x^4 are positive.

C

naveenhv · Answer

I agree. C is correct. 
Statement 1 tells us that x could be less than 0 or between 0 and 1. So insufficient.
Statement 2 tells us that x could be less than 0 or greater than 1. So insufficient.

Combining 1 and 2, we can deduce that x should be less than 0. So sufficient.

fluke · Answer

Can someone explain how to find the ranges using the number line approach (+ve and -ve curves); I find these types so tough. 1. x^3 < x^2 x^3 - x^2 < 0 x^2(x-1) < 0 Roots are; 0 and 1 Now; for a very small value of x; the above equation holds true So; the ranges are x<0, 01 According to the rule; we should consider the -ve curves for "<" sign so; x<0 and x>1. However, the correct ranges are x<0 or 01 doesn't; How does the rule change for even exponents and odd exponents. (2) x^3 < x^4 x^3 - x^4 <0 x^3(1-x) < 0 x^3(x-1) > 0 {Multiplying by -ve} roots 0 and 1 for a big value of x, the above equation holds good so; the ranges are; x>1, 0" x>1 x<0 This looks okay.

Bunuel · Answer

You should simplify x^3 < x^2 first. Reduce by x^2 (x^3 < x^2 means that x is not equal to zero so x^2>0) --> x<1, excluding one point x=0. So you can ignore the even power expressions in the approach you talk (just look whether zero is inclusive or not). For example, solve (x+3)(x+1)(x-1)(x+5)^2<0: Reduce by (x+5)^2 and note that x doesn't equal to -5' So we have (x+3)(x+1)(x-1)<0 and x doesn't equal to -5 --> roots -3, -1 and 1. Trying extreme value for x tells that in 4th range (when x>1) the whole expression is positive so it's negative in 3rd and 1st ranges (+-+-): -1

apoorv601 · Answer

C
From (1) x<0 or 0<x<1 
From (2) x<0 or x>1

From both .... x<0

Kimberly77 · Answer

Hi ,  gmat1220   apoorv601 
Thanks for the explanation but not quite sure how you derive below: Could you expand and explanin please? Thanks

From (1) x<0 or 0<x<1
From (2) x<0 or x>1

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Is x < 0 ? (1) x^3 < x^2 (2) x^3 < x^4

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