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100 points for $49 worth of Veritas practice GMATs FREE VERITAS PRACTICE GMAT EXAMS Earn 10 Points Per Post Earn 10 Points Per Thanks Earn 10 Points Per Upvote ## x ≠ 0. Is x^2>x^4? tagged by: Max@Math Revolution ##### This topic has 1 expert reply and 0 member replies ### GMAT/MBA Expert ## x ≠ 0. Is x^2>x^4? ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult [Math Revolution GMAT math practice question] 8.10 x ≠ 0. Is x^2>x^4? 1) x^2<1 2) x^2<2x _________________ Math Revolution Finish GMAT Quant Section with 10 minutes to spare. The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. Only$99 for 3 month Online Course
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Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question.

x^2>x^4
=> x^4 - x^2 < 0
=> x^2 ( x^2 - 1 ) < 0
=> ( x^2 - 1 ) < 0
=> ( x + 1 )( x - 1 ) < 0
=> -1 < x < 1

This is equivalent to condition 1).
Thus, condition 1) is sufficient.

Condition 2)
x^2<2x
=> x^2 - 2x < 0
=> x(x - 2) < 0
=> 0 < x < 2

In inequality questions, the law “Question is King” tells us that if the solution set of the question includes the solution set of the condition, then the condition is sufficient
However, the solution set of the question -1 < x < 1 does not include the solution set of the condition, 0 < x < 2. Thus, condition 2) is not sufficient.

_________________

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