Summer is Coming! Join the Game of Timers Competition to Win Epic Prizes. Registration is Open. Game starts Mon July 1st.

 It is currently 16 Jul 2019, 19:38 ### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  # If 0 < x < 1, what is the median of the values x, x^-1, x^2,

Author Message
TAGS:

### Hide Tags

Manager  Joined: 22 Sep 2005
Posts: 249
If 0 < x < 1, what is the median of the values x, x^-1, x^2,  [#permalink]

### Show Tags

5
25 00:00

Difficulty:   35% (medium)

Question Stats: 72% (01:32) correct 28% (01:38) wrong based on 851 sessions

### HideShow timer Statistics 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. $$x^3$$

Originally posted by netcaesar on 14 Nov 2006, 13:41.
Last edited by Bunuel on 24 Apr 2018, 05:19, edited 2 times in total.
Edited the question and added the OA
Manager  Joined: 13 Dec 2009
Posts: 212
Re: If 0 < x < 1, what is the median of the values x, x^-1, x^2,  [#permalink]

### Show Tags

6
1
5
gautamsubrahmanyam wrote:
If 0<x<1, what is the median of the values x,(x^-1),(x^2),(x^1/2),and (x^3)?

1) x
2) x^-1
3) x^2
4) x^1/2
5) x^3

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
_________________
##### General Discussion
Manager  Joined: 29 Aug 2006
Posts: 152
Re: If 0 < x < 1, what is the median of the values x, x^-1, x^2,  [#permalink]

### Show Tags

1
Rearranging the values for 0<x<1 in ascending order,

x^3,x^2, x,x^1/2,x^-1

Median will be x.
Manager  Joined: 10 Jul 2006
Posts: 63
Re: If 0 < x < 1, what is the median of the values x, x^-1, x^2,  [#permalink]

### Show Tags

4
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
Senior Manager  Joined: 24 Oct 2006
Posts: 319
Re: If 0 < x < 1, what is the median of the values x, x^-1, x^2,  [#permalink]

### Show Tags

enola wrote:
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

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.
GMAT Club Legend  Joined: 07 Jul 2004
Posts: 4527
Location: Singapore
Re: If 0 < x < 1, what is the median of the values x, x^-1, x^2,  [#permalink]

### Show Tags

2
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
Intern  Joined: 11 Aug 2013
Posts: 4
Re: If 0 < x < 1, what is the median of the values x, x^-1, x^2,  [#permalink]

### Show Tags

1
netcaesar wrote:
If 0<x<1, what is the median of the values x. x^-1, x^2, x^1/2 and x^3?

A) x

B) x^-1

C) x^2

D) x^1/2

E) x^3

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.
x^3, x^2, x, x^1/2, x^-1.
The mean is the middle number, hence x.
QA is A
Manager  S
Joined: 24 Oct 2013
Posts: 130
Location: India
Concentration: General Management, Strategy
WE: Information Technology (Computer Software)
Re: If 0 < x < 1, what is the median of the values x, x^-1, x^2,  [#permalink]

### Show Tags

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
Target Test Prep Representative D
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 6923
Location: United States (CA)
Re: If 0 < x < 1, what is the median of the values x, x^-1, x^2,  [#permalink]

### Show Tags

netcaesar wrote:
If 0 < x < 1, what is the median of the values x, x^-1, x^2, x^1/2 and x^3?

A. x
B. x^-1
C. x^2
D. x^1/2
E. x^3

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.

_________________

# Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

Manager  S
Joined: 28 Jun 2018
Posts: 134
Location: Bouvet Island
GMAT 1: 490 Q39 V18 GMAT 2: 640 Q47 V30 GMAT 3: 670 Q50 V31 GMAT 4: 700 Q49 V36 GPA: 4
Re: If 0 < x < 1, what is the median of the values x, x^-1, x^2,  [#permalink]

### Show Tags

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 : $$\frac{-1}{2}$$
$$(\frac{-1}{2})^2 = 1/4$$
$$(\frac{-1}{2})^3 = -1/8$$ -------------- $$(\frac{-1}{8}> \frac{-1}{2})$$ Re: If 0 < x < 1, what is the median of the values x, x^-1, x^2,   [#permalink] 06 Jan 2019, 02:42
Display posts from previous: Sort by

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