Is x x^2? (1) x x^2 (2) 1/x |x|

Question

Is √x > x^2 ? (1) x > x^2 (2) \frac{1}{x} > |x| Source: https://www.GMATinsight.com

SaquibHGMATWhiz · Answer

Solution: Pre-Analysis: We are asked if \sqrt{x} > x^2 or not The first thing to notice here is that since we have \sqrt{x} , the value of x cannot be negative and we are assuming that GMAT will not test us on imaginary numbers Now that we know x>0 , we have two regions to examine 0 x^2 satisfies x>1 which \sqrt{x} > x^2 doesn't satisfy Ultiately, we can say that the question is asking us if x falls in the range 0 x^2 This inequality x > x^2 clearly gives us the range 0 |x| Similar to statement 1, the above inequality is also only applicable in the range 0

Archit3110 · Answer

target is √x > x^2 or say √x-x^2>0 this is possible when 0 x^2 possible only for 0 |x| again possible when 0

chetan2u · Answer

Is √x > x^2 ? This will be true when 0 x^2 This means 0 |x| As \frac{1}{x} > |x| , 1/x >0 or x>0, which means |x|=x Cross multiply without changing sign 1>x*|x|……..x^2<1 . Thus x lies between -1 and 1. But as x>0, we get 0

Is x > x^2? (1) x > x^2 (2) 1/x > |x|

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