GMAT Changed on April 16th - Read about the latest changes here

 It is currently 27 May 2018, 08:40

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

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

Author Message
TAGS:

### Hide Tags

Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 5452
GMAT 1: 800 Q59 V59
GPA: 3.82
It’s well known that a company's profit=10,000x-50x2, where x is the n [#permalink]

### Show Tags

Updated on: 07 Apr 2017, 02:03
Expert's post
2
This post was
BOOKMARKED
00:00

Difficulty:

35% (medium)

Question Stats:

68% (01:17) correct 32% (01:12) wrong based on 174 sessions

### HideShow timer Statistics

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

_________________

MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only $79 for 3 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" 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. Math Expert Joined: 02 Sep 2009 Posts: 45459 Re: It’s well known that a company's profit=10,000x-50x2, where x is the n [#permalink] ### Show Tags 05 Apr 2017, 01:51 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 _________________ Manager Joined: 31 Jan 2017 Posts: 58 Location: India Concentration: Strategy, Leadership GMAT 1: 680 Q49 V34 GPA: 4 WE: Project Management (Energy and Utilities) Re: It’s well known that a company's profit=10,000x-50x2, where x is the n [#permalink] ### Show Tags 05 Apr 2017, 02:07 2 This post received KUDOS 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] _________________ __________________________________ Kindly press "+1 Kudos" if the post helped Manager Joined: 03 Jan 2016 Posts: 59 Location: India WE: Engineering (Energy and Utilities) Re: It’s well known that a company's profit=10,000x-50x2, where x is the n [#permalink] ### Show Tags 05 Apr 2017, 06:54 value of given expression increases as no of workers. So E Manager Joined: 01 Nov 2016 Posts: 69 Concentration: Technology, Operations Re: It’s well known that a company's profit=10,000x-50x2, where x is the n [#permalink] ### Show Tags 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? Manager Joined: 31 Jan 2017 Posts: 58 Location: India Concentration: Strategy, Leadership GMAT 1: 680 Q49 V34 GPA: 4 WE: Project Management (Energy and Utilities) Re: It’s well known that a company's profit=10,000x-50x2, where x is the n [#permalink] ### Show Tags 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. _________________ __________________________________ Kindly press "+1 Kudos" if the post helped Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 5452 GMAT 1: 800 Q59 V59 GPA: 3.82 Re: It’s well known that a company's profit=10,000x-50x2, where x is the n [#permalink] ### Show Tags 07 Apr 2017, 02:02 2 This post received KUDOS 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 _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$79 for 3 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"

BSchool Forum Moderator
Joined: 03 Aug 2016
Posts: 357
GMAT 1: 660 Q44 V38
GMAT 2: 690 Q46 V40
GPA: 3.9
WE: Information Technology (Consumer Products)
Re: It’s well known that a company's profit=10,000x-50x2, where x is the n [#permalink]

### Show Tags

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
_________________

My MBA Journey - https://smalldoubledouble.com

Math Expert
Joined: 02 Sep 2009
Posts: 45459
Re: It’s well known that a company's profit=10,000x-50x2, where x is the n [#permalink]

### Show Tags

10 Oct 2017, 20:55
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.
_________________
BSchool Forum Moderator
Joined: 03 Aug 2016
Posts: 357
GMAT 1: 660 Q44 V38
GMAT 2: 690 Q46 V40
GPA: 3.9
WE: Information Technology (Consumer Products)
Re: It’s well known that a company's profit=10,000x-50x2, where x is the n [#permalink]

### Show Tags

10 Oct 2017, 21:25
1
KUDOS
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
_________________

My MBA Journey - https://smalldoubledouble.com

DS Forum Moderator
Joined: 22 Aug 2013
Posts: 1145
Location: India
Re: It’s well known that a company's profit=10,000x-50x2, where x is the n [#permalink]

### Show Tags

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.

Manager
Joined: 04 May 2014
Posts: 162
Location: India
WE: Sales (Mutual Funds and Brokerage)
Re: It’s well known that a company's profit=10,000x-50x2, where x is the n [#permalink]

### Show Tags

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
Intern
Joined: 01 Oct 2017
Posts: 7
Re: It’s well known that a company's profit=10,000x-50x2, where x is the n [#permalink]

### Show Tags

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.

Sent from my iPhone using GMAT Club Forum mobile app
Re: It’s well known that a company's profit=10,000x-50x2, where x is the n   [#permalink] 29 Oct 2017, 12:58
Display posts from previous: Sort by