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It’s well known that a company's profit=10,000x50x2, 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=10,000x50x^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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Last edited by MathRevolution on 07 Apr 2017, 01:03, edited 1 time in total.



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Re: It’s well known that a company's profit=10,000x50x2, where x is the n [#permalink]
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05 Apr 2017, 00:51



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Re: It’s well known that a company's profit=10,000x50x2, 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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Re: It’s well known that a company's profit=10,000x50x2, 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



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Re: It’s well known that a company's profit=10,000x50x2, 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=10,000x50x2, 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=10,000x50x2, where x is the n [#permalink]
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07 Apr 2017, 01:02
==> 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=10,000x50x2, where x is the n [#permalink]
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10 Oct 2017, 19:50
Bunuel MathRevolutioni 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=10,000x50x2, where x is the n [#permalink]
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10 Oct 2017, 19:55



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Re: It’s well known that a company's profit=10,000x50x2, where x is the n [#permalink]
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10 Oct 2017, 20:25
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Bunuel wrote: mbsingh wrote: Bunuel MathRevolutioni 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=10,000x50x2, 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 [(x100)^2  10000] (I have written it in a square form, it is still the same)
= 50 [10000  (x100)^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 (x100) 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=10,000x50x2, 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 10000X10050(100)ˆ2=(10)ˆ65(10)ˆ5 X=5 10000X550(5)ˆ2=5(10)ˆ41250 X=50 10000X5050(50)ˆ2=5(10)ˆ5125(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=10,000x50x2, 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 10000X10050(100)ˆ2=(10)ˆ65(10)ˆ5 X=5 10000X550(5)ˆ2=5(10)ˆ41250 X=50 10000X5050(50)ˆ2=5(10)ˆ5125(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. Sent from my iPhone using GMAT Club Forum mobile app




Re: It’s well known that a company's profit=10,000x50x2, where x is the n
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