Is x 0? (1) x^3 + x^2 + x

Question

Is  x > 0 ?

(1)  x^3+x^2+x<0 
(2)  x^2<1

AlexKoh · Answer

The combined information is not sufficient to determine if x>0. The answer is (E) - "The statements together are NOT sufficient.

medheer_gautam · Answer

Given : A variable x that can either be an integer or a positive / negative fraction (as x is not specified) To determine : If x > 0 Note : Definitive yes or definitive no to be obtained for x>0 Statement A : - We are given that x^3 + x^2 + x< 0. - Factorizing this, x*(x^2+x+1)<0 - This leaves us with two options, x<0 & (x^2+x+1) >0 (Case 1) OR x>0 & (x^2+x+1)<0 (Case 2) - Case 1 seems good to go (For ex : x=-1 satisfies, x=-1/2 also satisfies and therefore, x clearly < 0) - Case 2 fails because there is no value of x >0 for which x^2+x+1<0 - Therefore, case 1 stays valid and we definitely know x>0. Statement A is sufficient *Automatically Eliminate Options C & E* Statement B : - We are given that x^2<1 - Therefore taking square roots on both sides, x clearly lies between 1 & -1 => For example, x can be 1/2 (here x>0) or -1/3 (here x<0) => We do not have a definitive yes or a definitive no for x>0 and therefore, Statement B is not sufficient *Eliminate Options B & D* => OA : A is the right Answer choice

LucienH · Answer

if statement A is < 0, this means that X has to be negative thus we can conclude the sign of X so A is sufficient

statement B doesn't help us because X could be any decimal value between -1 and 1 thus B is insufficient

Ans = A

Is x > 0? (1) x^3 + x^2 + x < 0 (2) x^2 < 1

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