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Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
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GMAT 1: 760 Q51 V42 GPA: 3.82

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1 00:00

Difficulty:

(N/A)

Question Stats: 36% (00:43) correct 64% (00:51) wrong based on 14 sessions

### HideShow timer Statistics The function $$y=px^2-4x+q$$ in the x-y plane attains a minimum value. What is the value of $$x$$?

1) $$p = 2$$
2) $$q = 5$$

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Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 7609
GMAT 1: 760 Q51 V42 GPA: 3.82

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Official Solution:

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

The first step of the VA (Variable Approach) method is to modify the original condition and the question, and then recheck the question.

$$y=px^2-4x+q$$ has a minimum value when $$x = -(-4)/2p = 2/p.$$ Thus, the question asks for the value of p.

Since only condition 1) gives us information about p, only condition 1) is sufficient.

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Intern  B
Joined: 16 Mar 2018
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Can someone please explain the logic behind reducing y=px(x2-4x)+Q to x=-(-4)/2P ?
Director  D
Joined: 08 Jun 2013
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2
Paugustin90 wrote:
Can someone please explain the logic behind reducing y=px(x2-4x)+Q to x=-(-4)/2P ?

For maxima and minima,

Take derivative of the equation and equate to 0 (rate of change is o at this point).

so dy/dx = 2px -4 = 0

x = 4/2p

Hope this helps!
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Intern  B
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1
Hi everyone,
Just wanted to say that the question here states " The function in the x-y plane attains a minimum value. What is THE value of x ? "
I believe the question should be rephrased to " What is that value of x" so that it becomes clear that we are talking about that x which will make this a minimum valued function.
Intern  Joined: 12 Aug 2018
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If the question had asked what is the value of x if the Function attained a Maximum value in the XY Plane? Please, advise.
Director  D
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2
Sharvil93 wrote:
If the question had asked what is the value of x if the Function attained a Maximum value in the XY Plane? Please, advise.

Sharvil93

zondice

The function y=px2−4x+q in the x-y plane attains a minimum value. What is the value of x?

1) p=2
2) q=5

Please note that y=px2−4x+q represents Parabola.

If p is positive then function will attain minima at some value of X (i.e. X= -b/2a) (Parabola open towards +ve Y- axis)

If p is negative then funcation will attain maxima at some value of X (i.e. X = -b/2a) ((Parabola open towards -ve Y- axis)

Hope this helps!!
_________________
Everything will fall into place…

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everything and everyone.
Never doubt, But Work on
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Intern  B
Joined: 10 Sep 2018
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Hi Everyone ,
Can someone pls elaborate the solution of this problem . I am unable to understand

Thanks
Director  D
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NCRanjan wrote:
Hi Everyone ,
Can someone pls elaborate the solution of this problem . I am unable to understand

Thanks

NCRanjan

https://gmatclub.com/forum/algebra-tips ... 75003.html

https://gmatclub.com/forum/what-is-the- ... 26302.html

Please go through above resources and my earlier post.

I think that will help.

Posted from my mobile device
_________________
Everything will fall into place…

There is perfect timing for
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Never doubt, But Work on
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NCRanjan wrote:
Hi Everyone ,
Can someone pls elaborate the solution of this problem . I am unable to understand

Thanks

This question relies on understanding that derivatives provide a maximum value

d/dx y = px^2 - 4x + q

0 = 2px - 4

p = 4/2x

If we know p we can figure out x.

For parabola equation

ax^2 + bx + c = y

We can find he value of x to be = -b/2a

Where b and a are the coeffecients in the formula

In this particular question it is like this

y = px^2 - 4x + q

b = -4
a = p

So x = -(-4)/2p = 4/2p

Hope it clears it out.

Posted from my mobile device
Intern  B
Joined: 08 Nov 2018
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Concentration: Accounting, Finance
GMAT 1: 380 Q32 V12 ### Show Tags

I think this the explanation isn't clear enough, please elaborate.
Manager  G
Joined: 10 Oct 2018
Posts: 182
GPA: 4

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Why everyone is solving through derivative (calculus) if it is not tested on GMAT? Not all are comfortable with it.
Can someone explain it in a simple way?

chetan2u VeritasKarishma pls help _________________
Senior Manager  P
Joined: 15 Feb 2018
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topper97
It's simply fancy language. Finding the maximum/minimum of a parabola that has the equation ax^2+bx+c follows the equation x = -b / 2a. I don't know calculus. I don't know how that equation is derived. It's simply one of the equations taught when learning quadratics in algebra class.

In saying that, it would probably help me to know how it is derived...

As a side note, I concur with zondice that the wording in this question is poor.
Intern  Joined: 15 Jan 2019
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I think this is a high-quality question and the explanation isn't clear enough, please elaborate.
Intern  Joined: 18 Nov 2014
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I think this is a high-quality question. Though the explanation is correct but requires more clarity on concepts
Intern  B
Joined: 24 Dec 2018
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Few things to know to undertsand the solution:
1. The derivative of a function equated to 0, can be solved to find the data point on the function at which it has slope=0.
2. The given quadratic equation is a parabola, hence it will have a slope =0 at only one point due to the parabolic curve shape.
3. Also the point of the function where slope =0 will be minimal if the parabola points upwards. And maximum if it points downwards.

Solving :
Apply dy/dx = 0 with the following derivative formulae:
d(x^2)/dx = 2x;
d(x)/dx = 1 ;
d(constant)/dx = 0

We get d(px^2-4x+q)/dx = 2px-4 = 0
=> x=4/2p = 2/p

Statement 1
p = 2
=> A parabola pointed upwards. As we have a positive value for the coefficient of x^2.
=> We can now find a value of x, which will be the minimal value of the curve in the x,y plane. M60-01   [#permalink] 22 Apr 2019, 20:07
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# M60-01

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