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

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

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05 Apr 2017, 00:23
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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
[Reveal] Spoiler: OA

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Last edited by MathRevolution on 07 Apr 2017, 01:03, edited 1 time in total.
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Posts: 43916
Re: It’s well known that a company's profit=10,000x-50x2, where x is the n [#permalink]

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05 Apr 2017, 00:51
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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Re: It’s well known that a company's profit=10,000x-50x2, where x is the n [#permalink]

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05 Apr 2017, 01:07
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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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Manager
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WE: Engineering (Energy and Utilities)
Re: It’s well known that a company's profit=10,000x-50x2, where x is the n [#permalink]

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05 Apr 2017, 05:54
value of given expression increases as no of workers.

So E
Manager
Joined: 01 Nov 2016
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Re: It’s well known that a company's profit=10,000x-50x2, where x is the n [#permalink]

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05 Apr 2017, 16:02
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]

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05 Apr 2017, 20:31
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.
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Re: It’s well known that a company's profit=10,000x-50x2, where x is the n [#permalink]

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07 Apr 2017, 01:02
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Expert's post
==> 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]

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10 Oct 2017, 19:50
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
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Re: It’s well known that a company's profit=10,000x-50x2, where x is the n [#permalink]

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10 Oct 2017, 19:55
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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Re: It’s well known that a company's profit=10,000x-50x2, where x is the n [#permalink]

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10 Oct 2017, 20:25
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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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Re: It’s well known that a company's profit=10,000x-50x2, where x is the n [#permalink]

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10 Oct 2017, 20:31
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]

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18 Oct 2017, 01:31
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
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Re: It’s well known that a company's profit=10,000x-50x2, where x is the n [#permalink]

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29 Oct 2017, 11:58
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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Re: It’s well known that a company's profit=10,000x-50x2, where x is the n   [#permalink] 29 Oct 2017, 11:58
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