If 0

Question

If 0 < x < 1, what is the median of the values  x ,  x^{-1} ,  x^2 ,  \sqrt{x}  and  x^3 ?

A.  x

B.  x^{-1}

C.  x^2

D.  \sqrt{x}

E.  x^3

sidhu4u · Accepted Answer

Easy way - pick a number for x. Let x =  \frac{1}{4}  (Taking  \frac{1}{4} because we need to do a square root here).
1)  x = \frac{1}{4} 
2)  x^-1 = \frac{1}{x} = 4 
3)  x^2 = \frac{1}{16} 
4)  \sqrt{x} = \frac{1}{2} 
5)  x^3 = \frac{1}{64} 
From the above 5 choices you can see that choices 2 and 4 are greater than x and choices 3 and 5 are less than x. Median must be the middle term when arranged in ascending order. x itself is the median as it is the middle value in ascending order

Priyah · Answer

Rearranging the values for 0<x<1 in ascending order,

x^3,x^2, x,x^1/2,x^-1

Median will be x.

enola · Answer

A for me too. To make the problem less confusing, I picked a number between 0 and 1 such as x = 1/4 and calculate:
x = 1/4
x^-1 = 4
x^2 = 1/16
x^(1/2) = 1/2
x^3 = 1/8. 

From this, rearrange the number and the median is 1/4, which is x. Answer A

Sumithra · Answer

Yup. I thought picking numbers would be easier and picked 0.5. Though I got the answer (a), I think fractions are easier than decimals.

ywilfred · Answer

x is a positive fraction. Pick any number, say 1/4

then 

x = 1/4
x^-1 = 1/x = 4
x^2 = 1/16
x^1/2 = 1/2
x^3 = 1/64

Rearranging in ascending order:

x^3, x^2, x, x^1/2, x^-1

Median = x

Ans A

tatarmalay · Answer

In info given by stem, basically we have a fraction.
So fraction value is increasing when it is under the root and decreasing when it is in power.
Just arrange answers according rules. 
x^3, x^2, x, x^1/2, x^-1.
The mean is the middle number, hence x.
QA is A

deepthit · Answer

for x between 0 and 1, we alwasy have a standard rule

X^3 < X^2 < X < root(X) < 1/x

following the above rule , when the above given terms can be arranged in the order and the mean is X

ScottTargetTestPrep · Answer

To find the median, we can let x be any value (fraction or decimal) between 0 and 1. So, let’s let x = ¼. Therefore:
 
x^-1 = (1/4)^-1 = 1/(1/4) = 4
 
x^2 = (1/4)^2 = 1/16
 
√x = √(1/4) = 1/2
 
x^3 = (1/4)^2 = 1/64
 
From the smallest to the largest, the order is:
 
x^3 = 1/64, x^2 = 1/16, x = 1/4, √x = 1/2, x^-1 = 4
 
Therefore, the median is x.
 
Note: We used ¼ as the value of x since it’s easy to take the square root of ¼, but any value between 0 and 1 will behave similarly, and x will always be the median.
 
Answer: A

blitzkriegxX · Answer

Important takeaway   - (especially important for DS questions)

<--------I---------I---------I---------->
 .......... -1 .......... 0 .......... 1

Between 0 to 1 -   
As the  exponent increases, the value decreases .

Example  :  \frac{1}{2} 
 (\frac{1}{2})^2 = 1/4 
 (\frac{1}{2})^3 = 1/8

Between -1 to 0 -   
As the  exponent increases, the value increases

Example  :  \frac{-1}{2} 
 (\frac{-1}{2})^2 = 1/4 
 (\frac{-1}{2})^3 = -1/8  --------------  (\frac{-1}{8}> \frac{-1}{2})

gmatcafe · Answer

If 0 < x < 1, what is the median of the values x, x^(-1), x^2, √x and x^3?
If 0 < x < 1, then x^(-1) will be greater than 1, so the largest number among our choices. √x will be greater than x but smaller than 1. x^2 and x^3 will be smaller than x. ----> x^3<x^2<x<√x<x^(-1) So x is the median.  A.

CrushTheQuant · Answer

Exponent rules are heavily tested on the GMAT... here's quick review of some of them, followed by an explanation of the correct answer on YouTube:

https://www.youtube.com/watch?v=95OHY24 ... uBg2fwokrI

bumpbot · Answer

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If 0 < x < 1, what is the median of the values x, x^-1, x^2,

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