Is x between 0 and 1? (1) -x

Question

Is x between 0 and 1?

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

Bunuel · Accepted Answer

Is x between 0 and 1? (1) -x < x^3: x^3+x>0 ; x(x^2+1)>0 ; x>0 (Since x^2 + 1 is always positive). Not sufficient. (2) x0 ; x(x-1)>0 ; Either x>1 or x<0 , so the answer the question whether x between 0 and 1 is always NO. Sufficient. Answer: B. 9. Inequalities Theory Inequalities Made Easy! Inequalities: Tips and hints Arithmetic with Inequalities Wavy Line Method Application - Complex Algebraic Inequalities Solving Quadratic Inequalities: Graphic Approach Inequalities - Quadratic Inequalities Graphic approach to problems with inequalities Inequalities trick INEQUATIONS(Inequalities) Part 1 INEQUATIONS(Inequalities) Part 2 Questions Inequality and absolute value questions from my collection DS Questions PS Questions For more check Ultimate GMAT Quantitative Megathread Hope it helps.

enigma123 · Answer

x<0

Shouldn't be x>0 because x(x-1) > 0?

Bunuel · Answer

x(x-1) > 0 --> roots are 0 and 1 --> ">" sign indicates that the solution lies to the left of a smaller root and to the right of the larger root: x<0 or x>1. Solving inequalities: x2-4x-94661.html#p731476 ( check this one first ) inequalities-trick-91482.html data-suff-inequalities-109078.html range-for-variable-x-in-a-given-inequality-109468.html?hilit=extreme#p873535 everything-is-less-than-zero-108884.html?hilit=extreme#p868863 Hope it helps.

Stiv · Answer

If someone could elaborate the first statement in more detail. From the statement I know that x(x^2 + 1)> 0, so x>0 and x^2 + 1> 1 isn't it?
Furthermore, I can conclude that x could be x>0 and x>1, so because I don't know the exact value of x the statement is insufficient.
Is that correct?

Bunuel · Answer

Not quite. The question asks: is 00 . So, we have that the product of two multiples, x and x^2+1 , is positive. Now, since the second multiple is always positive ( x^2+1= nonnegative +positive=positive ), then the first multiple must also be positive in order the product to be positive, therefore x>0 . So, from this statement, we cannot say whether 0

MathRevolution · Answer

Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution. Is x between 0 and 1? (1) -x < x^3 (2) x < x^2 There is only 1 variable (x), and 2 equations are given so there is high chance (D) will be our answer. If the range of the question includes that of the condition, the condition is sufficient. We can use this to solve questions quickly and accurately. The question asks whether 00, x(x^2+1)>0 (as x^2+1>0). From this we get x>0. This is insufficient as the range of the question does not include this range. From condition 2, x^2-x>0 x(x-1)>0, --> x<0 or 1

bumpbot · Answer

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Is x between 0 and 1? (1) -x < x^3 (2) x < x^2

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