GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

 It is currently 02 Jun 2020, 07:47 ### 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.  # The value of (1/x)-(4/√x)+4 is least when x =

Author Message
TAGS:

### Hide Tags

Director  V
Joined: 25 Dec 2018
Posts: 620
Location: India
Concentration: General Management, Finance
GMAT Date: 02-18-2019
GPA: 3.4
WE: Engineering (Consulting)
The value of (1/x)-(4/√x)+4 is least when x =  [#permalink]

### Show Tags

3 00:00

Difficulty:   65% (hard)

Question Stats: 53% (02:02) correct 47% (02:24) wrong based on 59 sessions

### HideShow timer Statistics

The value of (1/x)-(4/√x)+4 is least when x =

A. 1/√6
B. 1/4
C. 1/√2
D. 1/2
E. 1
Math Expert V
Joined: 02 Aug 2009
Posts: 8626
Re: The value of (1/x)-(4/√x)+4 is least when x =  [#permalink]

### Show Tags

1
mangamma wrote:
The value of (1/x)-(4/√x)+4 is least when x =

A. 1/√6
B. 1/4
C. 1/√2
D. 1/2
E. 1

Since we have √x, X has to be positive, so let x=y^2..
So (1/x)-(4/√x)+4=(1/y^2)-(4/y)+4=$$\frac{4y^2-4y+1}{y^2}=\frac{(2y-1)^2}{y^2}$$..
Least value here will be 0 when numerator is 0. (2y-1)^2 will be 0 at y=1/2..
Thus x=y^2=(1/2)^2=1/4..

B

If you are clueless, just see here X is, it is in the denominator...
To make the term lowest, we have to maximize the - term, that is -(4/√x).
And X is the denominator, so we have to make the denominator the least.
In choices 1/4 is the least.
Need not be true always, but will increase the probability of answering correctly if you have nowhere to go.
_________________
Manager  S
Joined: 23 Jul 2019
Posts: 172
Location: Austria
GPA: 3.9
The value of (1/x)-(4/√x)+4 is least when x =  [#permalink]

### Show Tags

Can someone explain this in a bit more detail? The approach seems really advanced and is not something I would arrive logically.
What am I missing I had a approach where I just plugged in numbers and it was clear that it has to be either 1 / sqrt (6) or 1 / 4
From here it got a bit messy.

But I estimated sqrt 6 as 2.50 and with a bit of guesstimating 1/4 gave the least value.

Think I could not do it under time pressure with this calculation.
_________________
Let's get some The value of (1/x)-(4/√x)+4 is least when x =   [#permalink] 23 Sep 2019, 23:50

# The value of (1/x)-(4/√x)+4 is least when x =  