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# The longevity of a certain metal construction is determined by the fol

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Math Expert
Joined: 02 Sep 2009
Posts: 58333
The longevity of a certain metal construction is determined by the fol  [#permalink]

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03 Nov 2014, 10:01
00:00

Difficulty:

5% (low)

Question Stats:

90% (01:24) correct 10% (01:55) wrong based on 94 sessions

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Tough and Tricky questions: Word Problems.

The longevity of a certain metal construction is determined by the following formula: $$l = (7.5 - x)^4 + 8.97^c$$, where l is the longevity of the construction, in years, x is the density of the underlying material, in g/cm^3, and c is a positive constant equal to 1.05 for this type of metal constructions. For what value of density, x, expressed in g/cm^3, will the metal construction have minimal longevity?

A. -7.5
B. 0
C. 7.5
D. 15
E. 75

Kudos for a correct solution.

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Joined: 10 Jan 2014
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GMAT 1: 600 Q40 V31
Re: The longevity of a certain metal construction is determined by the fol  [#permalink]

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03 Nov 2014, 11:08
1
Bunuel wrote:

Tough and Tricky questions: Word Problems.

The longevity of a certain metal construction is determined by the following formula: $$l = (7.5 - x)^4 + 8.97^c$$, where l is the longevity of the construction, in years, x is the density of the underlying material, in g/cm^3, and c is a positive constant equal to 1.05 for this type of metal constructions. For what value of density, x, expressed in g/cm^3, will the metal construction have minimal longevity?

A. -7.5
B. 0
C. 7.5
D. 15
E. 75

Kudos for a correct solution.

My Solution:

Is the answer C?
Acc to the equation 8.97^ C is constant. So The value of L will be minimal when (7.5 - x)^4 =0.
Solving: x= 7.5
Plugging the value: (7.5 - 7.5)^4 = 0
Checking: (7.5 - (-7.5))^4 =(15)^4 (too big)
Since the power is even, the result will be positive. So B, D, E give bigger values.

The question is tricky so I think I am missing some key info. Am I?
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Joined: 19 Oct 2014
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Re: The longevity of a certain metal construction is determined by the fol  [#permalink]

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03 Nov 2014, 11:56
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1
IMO the answer is C.

To minimize this we need to min $$(7.5-x)^4$$.

The min value of which is 0 when x = 7.5

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Re: The longevity of a certain metal construction is determined by the fol  [#permalink]

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03 Nov 2014, 23:07
1

For minimum longevity, equate

$$(7.5-x)^4 = 0$$

x = 7.5
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Re: The longevity of a certain metal construction is determined by the fol  [#permalink]

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01 Apr 2018, 03:39
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Re: The longevity of a certain metal construction is determined by the fol   [#permalink] 01 Apr 2018, 03:39
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# The longevity of a certain metal construction is determined by the fol

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