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

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GMATinsight
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If x > 0, What is the median of x^2, x and √x? 1) x^2-1 < 1 [#permalink] New post   Updated on: 29 Mar 2021, 23:37
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If x > 0, What is the median of \(x^2\), \(x^3\) and \(√x\)?

1) \(x^2-1 < 1\)
2) \(x < \frac{1}{x}\)

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B

Originally posted by GMATinsight on 25 Mar 2021, 23:33.
Last edited by GMATinsight on 29 Mar 2021, 23:37, edited 1 time in total.
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chetan2u
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Re: If x > 0, What is the median of x^2, x and √x? 1) x^2-1 < 1 [#permalink] New post   26 Mar 2021, 00:39
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GMATinsight wrote:
If x > 0, What is the median of \(x^2\), \(x\) and \(√x\)?

1) \(x^2-1 < 1\)
2) \(x < \frac{1}{x}\)


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) \(0<x<1\)
The value decreases as the power is increased. So \(x^2<x<√x\). Median is x.
B) \(x>1\)
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.
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Re: If x > 0, What is the median of x^2, x and √x? 1) x^2-1 < 1 [#permalink] New post   Updated on: 26 Mar 2021, 22:32
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

GMATinsight wrote:
If x > 0, What is the median of \(x^2\), \(x\) and \(√x\)?

1) \(x^2-1 < 1\)
2) \(x < \frac{1}{x}\)


Originally posted by Archit3110 on 26 Mar 2021, 01:45.
Last edited by Archit3110 on 26 Mar 2021, 22:32, edited 2 times in total.
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chetan2u
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Re: If x > 0, What is the median of x^2, x and √x? 1) x^2-1 < 1 [#permalink] New post   26 Mar 2021, 02:18
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Archit3110 wrote:
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
which is possible only when values of x falls in range 0<x<1 ; therefore sufficient that x is median for x^2<x<√x

#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 D

GMATinsight wrote:
If x > 0, What is the median of \(x^2\), \(x\) and \(√x\)?

1) \(x^2-1 < 1\)
2) \(x < \frac{1}{x}\)



In statement I, x^2<2 means the range is 0<x<\(\sqrt{2}\)
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Re: If x > 0, What is the median of x^2, x and √x? 1) x^2-1 < 1 [#permalink]
26 Mar 2021, 02:18
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