If x^3 x^2 ?

Question

If x^3 < x, is x > x^2 ? (1) x > -5 (2) x < -2

Bunuel · Accepted Answer

If x^3 < x, is x > x^2 ? Given: x^3 < x --> (x+1)x(x-1)<0 --> x<-1 (firs range) or 0x^2 ? --> x(1-x)>0 ? Is 0 -5 --> x can be from the first range (for example, if x=-3), but x can be from the second range too (for example, if x=1/2). Not sufficient. (2) x < -2 --> x cannot be from the second range. Sufficient. Answer: B. Theory on Inequalities: x2-4x-94661.html#p731476 inequalities-trick-91482.html data-suff-inequalities-109078.html range-for-variable-x-in-a-given-inequality-109468.html everything-is-less-than-zero-108884.html graphic-approach-to-problems-with-inequalities-68037.html All DS Inequalities Problems to practice: search.php?search_id=tag&tag_id=184 All PS Inequalities Problems to practice: search.php?search_id=tag&tag_id=189 700+ Inequalities problems: inequality-and-absolute-value-questions-from-my-collection-86939.html Hope this helps.

HarveyS · Answer

Make a table...

x | x^3
--------
-2| -8 --- True

1/2| 1/8 ----- True

2 | 8 ---- false

2 conditions

Stm 1- Can be any value.... Not Suff

Stm 2- Less that -2 -- Suff

B

theventurer · Answer

If x^3 < x, is x > x^2 ? 1. x > -5 2. x < -2

Bowtye · Answer

Is the OA really E? I am inclined to say the answer is B. If x is less than -2 then x is negative with an absolute value greater than 1 (where the gmat tries to trick you with decimals being greater than or less than). The square of any number (technically any real number, which is all the gmat is concerned with) is positive. X^2 > X.

Unless I am missing something

Unless I am missing something

Bunuel · Answer

Merging topics.

Yes, the correct answer is B.

VikashAlex · Answer

Hi, as per given statement: x^3 < x will be valid in two conditions: 1) x values will lie between 0 to 1. 2) x values will lie less than -1. Question asks: x > x^2 ....means....is x lie between -1 to 1? Stat1: x > -5 that means x may be -4 which will satisfy the condition( condition 2 mentioned above) and -4 does not lie between -1 to 1. Hence ans for this is NO . now take x value 0.5 which satisfy the condition( condition 1 mentioned above) and 0.5 lies between -1 to 1. Thus ans for this is Yes . We can see that for this option there is not any definite answer. Hence this option is insufficient . Stat2: x < -2 hence what ever the value we will take will less than -1 (hence satisfies the condition 2 mentioned above) and will never fall in between -1 to 1. Hence ans for this is definite, which is NO . Thus this option suffice the data. Sufficient +1 kudos if it helped you

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. If x^3 < x, is x > x^2 ? (1) x > -5 (2) x < -2 For questions regarding inequalities, if the range of the question includes that of the condition, the condition becomes the answer. If we modify the question, x^3-x<0, x(x^2-1)<0, x(x-1)(x+1)<0 ==> x<-1, 0 x(x-1)<0? ==> 0-5 2) x<-2 one variable (x), we therefore need one equation. Two equations are given, so there is high chance (D) will be our answer. 1) the question does not include the range of -5

CEdward · Answer

If x^3 < x, is x > x^2 ?

x^3 < x implies that x is either a fraction or is negative. But, we don't know which one so x > x^2 comes out differently depending on our answer to that question.

(1) x > -5
Insufficient since x can be a fraction between - 1 < x < 1 or can be negative.

(2) x < -2
Sufficient, x is necessarily negative. Therefore, x IS NOT greater than x^2.

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If x^3 < x, is x > x^2 ?

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