It’s well known that a company's profit=10,000x-50x2, where x is the n : Problem Solving (PS)

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MathRevolution

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It’s well known that a company's profit=10,000x-50x2, where x is the n [#permalink]

Updated on: 07 Apr 2017, 02:03

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It’s well known that a company's profit=10,000x-50x^2, where x is the number of workers. If the profit of the company is the greatest, what is the value of x?

A. 5
B. 10
C. 50
D. 80
E. 100

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Originally posted by MathRevolution on 05 Apr 2017, 01:23.
Last edited by MathRevolution on 07 Apr 2017, 02:03, edited 1 time in total.

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Spartan85

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Re: It’s well known that a company's profit=10,000x-50x2, where x is the n [#permalink]

05 Apr 2017, 02:07

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Answer : [E]

To find Max or Min of a polynomial f(x), Equate f'(x)=0

f(x) = 10,000x - 50x^2

f'(x) = 10,000 - 50*2x = 0 [differentiating ]

100x = 10,000

x=100

[ to cross check if it is truely max f"(x) should be negative = -100]

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MathRevolution

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Re: It’s well known that a company's profit=10,000x-50x2, where x is the n [#permalink]

07 Apr 2017, 02:02

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==> From \(y=f(x)=ax^2+bx+c\), if \(x=\frac{-b}{2a}\), f(x) becomes either maximum or minimum. Thus, profit=\(-50x^2+10,000x\), and in order for the profit to become the greatest, you get \(x=\frac{-10,000}{2(-50)}=100\).

The answer is E.
Answer: E

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Re: It’s well known that a company's profit=10,000x-50x2, where x is the n [#permalink]

10 Oct 2017, 21:25

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Bunuel wrote:

mbsingh wrote:

Bunuel MathRevolution

i got stumped by similar questions before. So when the question says 10,000x does that mean x is multiplied by 10,000 or is it the units digit ?
I know 10,000 (thousands comma separator) should give it away but other questions dont have it sometimes

and also for 50x^2 is that x squared or (50X) squared.

Thanks

10000x always means 10000*x. If it were an units digit it would have been explicitly mentioned.

50x^2 always means 50*x^2. If it were (50x)^2 would have been written (50x)^2.

Thanks Bunuel. I wish i could borrow your brain for exam day. Not a bad trade off, mine comes with long list of pick up lines and quality stuff for stand up comedy :D

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Bunuel

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Re: It’s well known that a company's profit=10,000x-50x2, where x is the n [#permalink]

05 Apr 2017, 01:51

Expert Reply

MathRevolution wrote:

It’s well known that a company's profit=10,000x-50x^2, where x is the number of workers. If the profit of the company is the greatest, what is the value of x?

A. 5
B. 10
C. 50
D. 80

E. 100

This is almost the same exact question as this one: https://gmatclub.com/forum/it-s-well-kn ... 27127.html
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gvvsnraju@1

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Re: It’s well known that a company's profit=10,000x-50x2, where x is the n [#permalink]

05 Apr 2017, 06:54

value of given expression increases as no of workers.

So E

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joondez

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Re: It’s well known that a company's profit=10,000x-50x2, where x is the n [#permalink]

05 Apr 2017, 17:02

Spartan85 wrote:

Answer : [E]

To find Max or Min of a polynomial f(x), Equate f'(x)=0

f(x) = 10,000x - 50x^2

f'(x) = 10,000 - 50*2x = 0 [differentiating ]

100x = 10,000

x=100

[ to cross check if it is truely max f"(x) should be negative = -100]

Haha this is how I solved the question too, but this is calculus. I think GMAT does not require calculus? Is this a realistic question for the test?

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Re: It’s well known that a company's profit=10,000x-50x2, where x is the n [#permalink]

05 Apr 2017, 21:31

joondez wrote:

Spartan85 wrote:

Answer : [E]

To find Max or Min of a polynomial f(x), Equate f'(x)=0

f(x) = 10,000x - 50x^2

f'(x) = 10,000 - 50*2x = 0 [differentiating ]

100x = 10,000

x=100

[ to cross check if it is truely max f"(x) should be negative = -100]

Haha this is how I solved the question too, but this is calculus. I think GMAT does not require calculus? Is this a realistic question for the test?

Assuming that this type of problem may come on the GMAT, knowing only this little part of Calculus is highly recommended. :-D

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Re: It’s well known that a company's profit=10,000x-50x2, where x is the n [#permalink]

10 Oct 2017, 20:50

Bunuel MathRevolution

i got stumped by similar questions before. So when the question says 10,000x does that mean x is multiplied by 10,000 or is it the units digit ?
I know 10,000 (thousands comma separator) should give it away but other questions dont have it sometimes

and also for 50x^2 is that x squared or (50X) squared.

Thanks

L

Bunuel

Math Expert

Joined: 02 Sep 2009

Posts: 92762

Re: It’s well known that a company's profit=10,000x-50x2, where x is the n [#permalink]

10 Oct 2017, 20:55

Expert Reply

mbsingh wrote:

Bunuel MathRevolution

i got stumped by similar questions before. So when the question says 10,000x does that mean x is multiplied by 10,000 or is it the units digit ?
I know 10,000 (thousands comma separator) should give it away but other questions dont have it sometimes

and also for 50x^2 is that x squared or (50X) squared.

Thanks

10000x always means 10000*x. If it were an units digit it would have been explicitly mentioned.

50x^2 always means 50*x^2. If it were (50x)^2 would have been written (50x)^2.
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amanvermagmat

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Re: It’s well known that a company's profit=10,000x-50x2, where x is the n [#permalink]

10 Oct 2017, 21:31

well we can do it this way also:

10000x - 50x^2 = -50 (x^2 - 10000x/50) = -50 (x^2 - 200x) (I have taken -50 outside common)

= -50 [(x-100)^2 - 10000] (I have written it in a square form, it is still the same)

= 50 [10000 - (x-100)^2] (Now removed the minus sign outside and changed inside, so still same)

Now, if we observe, the MAX value of this expression will be when (x-100) becomes '0' (zero), and that will only happen when x=100.

So E answer

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Re: It’s well known that a company's profit=10,000x-50x2, where x is the n [#permalink]

18 Oct 2017, 02:31

It is easier to plug the value of x given in the answer choices.
Start with the max then the min and the middle. we will get our range.
X=100
10000X100-50(100)ˆ2=(10)ˆ6-5(10)ˆ5
X=5
10000X5-50(5)ˆ2=5(10)ˆ4-1250
X=50
10000X50-50(50)ˆ2=5(10)ˆ5-125(10)ˆ4
The highest power of 10 we get when X=100

Amyy2692

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Re: It’s well known that a company's profit=10,000x-50x2, where x is the n [#permalink]

29 Oct 2017, 12:58

gps5441 wrote:

It is easier to plug the value of x given in the answer choices.
Start with the max then the min and the middle. we will get our range.
X=100
10000X100-50(100)ˆ2=(10)ˆ6-5(10)ˆ5
X=5
10000X5-50(5)ˆ2=5(10)ˆ4-1250
X=50
10000X50-50(50)ˆ2=5(10)ˆ5-125(10)ˆ4
The highest power of 10 we get when X=100

precisely how I got my answer. Coz the question asks for the “maximum” value. Sure got taken aback when I saw people using calculus.

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Its well known that a company's profit=10,000x-50x2, where x is the n [#permalink]

29 Jul 2023, 10:30

company's profit P=10,000x-50x^2

Using calculus P max when dP/dx = 0

=> dP/dx=10,000-100x=0

=>x=100
Hence E

Therefore Pmax = P(x=100)=10,000*100-50*100*100=500,000

gmatclubot

Its well known that a company's profit=10,000x-50x2, where x is the n [#permalink]

29 Jul 2023, 10:30

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