If x 0, What is the median of x^2, x and √x? 1) x^2-1

Question

If x > 0, What is the median of x^2 , x^3 and √x ? 1) x^2-1 < 1 2) x < \frac{1}{x} Source : https://www.GMATinsight.com

chetan2u · Answer

As there are 3 terms, one of the term will be the median. Since x>0, there are two ranges that come into play when we increase the power of the number x, and in each case, x is the median. A) 01 The value increases as the power is increased. So x^2>x>√x . Median is x. So in each case, x is the median. Even if x=1, all three values are 1, and all three values including x are the median. Also, the question mentions ÏS", so we are looking at just one of them being median, and x is the answer. We do not require statements I and II to answer this. It is always x.

Archit3110 · Answer

point to note that for values of x between 0 and 1 ; x^2<x<√x

target What is the median of  x^2 ,  x  and  √x ?

#1
 x^2-1 < 1 
x^2<2
x<√2
which is possible only when values of x falls in range 0<x<√2 ; 0<X<1.41 therefore sufficient that x is median for values 0<X<1 but not valid for values 1<X<1.14 insufficient

#2
 x < \frac{1}{x} 
or say x^2<1

again this is possible only when values of x falls in range 0<x<1 ; therefore sufficient that x is median for x^2<x<√x
option B

chetan2u · Answer

In statement I, x^2<2 means the range is 0<x< \sqrt{2}

If x > 0, What is the median of x^2, x and √x? 1) x^2-1 < 1

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