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M60-01

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M60-01  [#permalink]

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New post 11 Jun 2018, 02:00
00:00
A
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D
E

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Question Stats:

80% (00:27) correct 20% (00:00) wrong based on 5 sessions

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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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Re M60-01  [#permalink]

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New post 11 Jun 2018, 02:00
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.

Therefore, A is the answer.



Answer: A
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Re: M60-01  [#permalink]

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New post 31 Jul 2018, 11:50
Can someone please explain the logic behind reducing y=px(x2-4x)+Q to x=-(-4)/2P ?
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Re: M60-01  [#permalink]

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New post 03 Aug 2018, 23:18
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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Re: M60-01  [#permalink]

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New post 10 Aug 2018, 13:05
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.
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Re: M60-01  [#permalink]

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New post 17 Aug 2018, 22:22
If the question had asked what is the value of x if the Function attained a Maximum value in the XY Plane? Please, advise.
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M60-01  [#permalink]

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New post 18 Aug 2018, 01:30
1
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!!
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M60-01 &nbs [#permalink] 18 Aug 2018, 01:30
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