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

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Director
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]

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19 Apr 2019, 07:54
3
00:00

Difficulty:

65% (hard)

Question Stats:

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

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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
Joined: 02 Aug 2009
Posts: 8626
Re: The value of (1/x)-(4/√x)+4 is least when x =  [#permalink]

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19 Apr 2019, 22:55
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.
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Joined: 23 Jul 2019
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The value of (1/x)-(4/√x)+4 is least when x =  [#permalink]

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23 Sep 2019, 23:50
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.
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The value of (1/x)-(4/√x)+4 is least when x =   [#permalink] 23 Sep 2019, 23:50