The longevity of a certain metal construction is determined by the following formula:
l = (7.5 - x)^4 + 8.97c, where l is the longevity of the construction, in years, x is the density of the underlying material, in g/cm3, 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/cm3, will the metal construction have minimal longevity?
A. -7.5
B. 0
C. 7.5
D.15
E. 75
Source : MGMAT CAT
Need different approaches
Longevity
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Which MGMAT guide is this from : Word Translations or Number Properties ? Please also mention the Edition .bhumika.k.shah wrote:
Source : MGMAT CAT
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Its from MGMAT CAT and not QB
Hence NO edition as such...
CAT = Computer Adaptive Test.
Hence NO edition as such...
CAT = Computer Adaptive Test.
Haldiram Bhujiawala wrote:Which MGMAT guide is this from : Word Translations or Number Properties ? Please also mention the Edition .bhumika.k.shah wrote:
Source : MGMAT CAT
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Such probs can be solved using derivative,Which I think the GMAt doesn't test.
I = (7.5 - x)^4 + 8.97c Taking derivative on both side I get
dI/dx = 4*(7.5 - x)^3
Now for least value of L means dI/dx = 0
means x = 7.5
If there is any other solution please let us know .
I = (7.5 - x)^4 + 8.97c Taking derivative on both side I get
dI/dx = 4*(7.5 - x)^3
Now for least value of L means dI/dx = 0
means x = 7.5
If there is any other solution please let us know .
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kstv's solution is the fastest way to solve. Common sense/logic goes a long way to saving time on the GMAT.gauravgundal wrote:Such probs can be solved using derivative,Which I think the GMAt doesn't test.
I = (7.5 - x)^4 + 8.97c Taking derivative on both side I get
dI/dx = 4*(7.5 - x)^3
Now for least value of L means dI/dx = 0
means x = 7.5
If there is any other solution please let us know .
Whenever a question asks us to minimize or maximize something, think through the task: what other variable should I minimize or maximize to reach my goal?
As an aside, you definitely don't need to know any calculus or high end functions (e.g. limits) for the GMAT.
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l = (7.5-x)^4 + 8.97^c , where c is a constant
dl/dx = 0 to minimze l
dl/dx = 4(7.5-x)^3 + 0 = 0
dl/dx = 4(7.5-x)^3, x = 7.5 for dl/dx = 0 and l to be minimized
dl/dx = 0 to minimze l
dl/dx = 4(7.5-x)^3 + 0 = 0
dl/dx = 4(7.5-x)^3, x = 7.5 for dl/dx = 0 and l to be minimized
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The longevity of a certain metal construction is determined by the following formula:
l = (7.5 - x)^4 + 8.97c, where l is the longevity of the construction, in years, x is the density of the underlying material, in g/cm3, 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/cm3, will the metal construction have minimal longevity?
A. -7.5
B. 0
C. 7.5
D.15
E. 75
l is a function of x and c but since c is constant therefore the entire focus is x
l will be minimum when (7.5 - x)^4 is minimum but since it's a perfect squant and the minimum value of a perfect square is "0" therefore (7.5 - x)^4 must be "0" for smallest value of l
(7.5 - x)^4 = 0 @x=7.5 ANSWER Option: C
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One request and suggestion to GMAT aspirants
"Refrain from higher maths like Differentiation, Calculus, Trigonometry etc. for keeping the right orientation and limited required concepts to Beat the GMAT"
All the best!!!
"Refrain from higher maths like Differentiation, Calculus, Trigonometry etc. for keeping the right orientation and limited required concepts to Beat the GMAT"
All the best!!!
"GMATinsight"Bhoopendra Singh & Sushma Jha
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To answer this question, we need to minimize the value of l = (7.5 - x)^4 + (8.97)^1.05. Since we do not need to determine the actual minimum longevity, we do not need to find the value of the second component in our formula, (8.97)^1.05, which will remain constant for any level of x. Therefore, to minimize longevity, we need to minimize the value of the first component in our formula,
i.e. (7.5 - x)^4. Since we are raising the expression (7.5 - x) to an even exponent, 4, the value of
(7.5 - x)4 will always be non-negative, i.e. positive or zero. Thus, to minimize this outcome, we need to find the value of x for which (7.5 - x)^4 = 0.
(7.5 - x)^4 = 0
7.5 - x = 0
x = 7.5
Therefore, the metal construction will have minimal longevity for the value of x = 7.5, i.e. when the density of the underlying material will be equal to 7.5 g/cm3.
The correct answer is C.
i.e. (7.5 - x)^4. Since we are raising the expression (7.5 - x) to an even exponent, 4, the value of
(7.5 - x)4 will always be non-negative, i.e. positive or zero. Thus, to minimize this outcome, we need to find the value of x for which (7.5 - x)^4 = 0.
(7.5 - x)^4 = 0
7.5 - x = 0
x = 7.5
Therefore, the metal construction will have minimal longevity for the value of x = 7.5, i.e. when the density of the underlying material will be equal to 7.5 g/cm3.
The correct answer is C.
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Also, since the OP asked for multiple approaches, let me give you an easy (= mindless) one: try the answers.
Since l = (7.5 - x)� + 8.97 * 1.05, the only part we need to minimize is the unknown, (7.5 - x)�.
Plugging in the answers, we get
A:: 15�
B:: 7.5�
C:: 0�
D:: (-7.5)�
E:: (-67.5)�
C is clearly smallest, so we're set.
Since l = (7.5 - x)� + 8.97 * 1.05, the only part we need to minimize is the unknown, (7.5 - x)�.
Plugging in the answers, we get
A:: 15�
B:: 7.5�
C:: 0�
D:: (-7.5)�
E:: (-67.5)�
C is clearly smallest, so we're set.