GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 11 Dec 2018, 19:10

Close

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
Your Progress

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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel
Events & Promotions in December
PrevNext
SuMoTuWeThFrSa
2526272829301
2345678
9101112131415
16171819202122
23242526272829
303112345
Open Detailed Calendar
  • Free GMAT Prep Hour

     December 11, 2018

     December 11, 2018

     09:00 PM EST

     10:00 PM EST

    Strategies and techniques for approaching featured GMAT topics. December 11 at 9 PM EST.
  • The winning strategy for 700+ on the GMAT

     December 13, 2018

     December 13, 2018

     08:00 AM PST

     09:00 AM PST

    What people who reach the high 700's do differently? We're going to share insights, tips and strategies from data we collected on over 50,000 students who used examPAL.

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

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Math Revolution GMAT Instructor
User avatar
V
Joined: 16 Aug 2015
Posts: 6620
GMAT 1: 760 Q51 V42
GPA: 3.82
Premium Member
It’s well known that a company's profit=10,000x-50x2, where x is the n  [#permalink]

Show Tags

New post Updated on: 07 Apr 2017, 01:03
00:00
A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

71% (01:45) correct 29% (02:01) wrong based on 180 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 $99 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, 00:23.
Last edited by MathRevolution on 07 Apr 2017, 01:03, edited 1 time in total.
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 51100
Re: It’s well known that a company's profit=10,000x-50x2, where x is the n  [#permalink]

Show Tags

New post 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
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Manager
Manager
User avatar
G
Joined: 31 Jan 2017
Posts: 58
Location: India
Concentration: Strategy, Leadership
GMAT 1: 680 Q49 V34
GPA: 4
WE: Project Management (Energy and Utilities)
Premium Member Reviews Badge
Re: It’s well known that a company's profit=10,000x-50x2, where x is the n  [#permalink]

Show Tags

New post 05 Apr 2017, 01:07
2
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
Manager
avatar
S
Joined: 03 Jan 2016
Posts: 59
Location: India
WE: Engineering (Energy and Utilities)
GMAT ToolKit User
Re: It’s well known that a company's profit=10,000x-50x2, where x is the n  [#permalink]

Show Tags

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

So E
Manager
Manager
avatar
B
Joined: 01 Nov 2016
Posts: 66
Concentration: Technology, Operations
Re: It’s well known that a company's profit=10,000x-50x2, where x is the n  [#permalink]

Show Tags

New post 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?
Manager
Manager
User avatar
G
Joined: 31 Jan 2017
Posts: 58
Location: India
Concentration: Strategy, Leadership
GMAT 1: 680 Q49 V34
GPA: 4
WE: Project Management (Energy and Utilities)
Premium Member Reviews Badge
Re: It’s well known that a company's profit=10,000x-50x2, where x is the n  [#permalink]

Show Tags

New post 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. :-D
_________________

__________________________________
Kindly press "+1 Kudos" if the post helped :)

Math Revolution GMAT Instructor
User avatar
V
Joined: 16 Aug 2015
Posts: 6620
GMAT 1: 760 Q51 V42
GPA: 3.82
Premium Member
Re: It’s well known that a company's profit=10,000x-50x2, where x is the n  [#permalink]

Show Tags

New post 07 Apr 2017, 01:02
2
==> 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 $99 for 3 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"

Retired Moderator
avatar
G
Joined: 03 Aug 2016
Posts: 353
Location: Canada
GMAT 1: 660 Q44 V38
GMAT 2: 690 Q46 V40
GPA: 3.9
WE: Information Technology (Consumer Products)
Premium Member
Re: It’s well known that a company's profit=10,000x-50x2, where x is the n  [#permalink]

Show Tags

New post 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
_________________

My MBA Journey - https://smalldoubledouble.com

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 51100
Re: It’s well known that a company's profit=10,000x-50x2, where x is the n  [#permalink]

Show Tags

New post 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.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Retired Moderator
avatar
G
Joined: 03 Aug 2016
Posts: 353
Location: Canada
GMAT 1: 660 Q44 V38
GMAT 2: 690 Q46 V40
GPA: 3.9
WE: Information Technology (Consumer Products)
Premium Member
Re: It’s well known that a company's profit=10,000x-50x2, where x is the n  [#permalink]

Show Tags

New post 10 Oct 2017, 20:25
1
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
avatar
P
Joined: 21 Aug 2013
Posts: 1412
Location: India
Premium Member
Re: It’s well known that a company's profit=10,000x-50x2, where x is the n  [#permalink]

Show Tags

New post 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
Manager
Manager
avatar
B
Joined: 03 May 2014
Posts: 160
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

New post 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
Intern
Intern
avatar
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

New post 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.


Sent from my iPhone using GMAT Club Forum mobile app
GMAT Club Bot
Re: It’s well known that a company's profit=10,000x-50x2, where x is the n &nbs [#permalink] 29 Oct 2017, 11:58
Display posts from previous: Sort by

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

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


Copyright

GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.