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

It is currently 19 Oct 2018, 22:03

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

During an experiment, the growth rate of a bacteria colony

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

Hide Tags

Senior Manager
Senior Manager
User avatar
Joined: 21 Oct 2013
Posts: 420
During an experiment, the growth rate of a bacteria colony  [#permalink]

Show Tags

New post Updated on: 27 Aug 2014, 05:02
2
5
00:00
A
B
C
D
E

Difficulty:

  15% (low)

Question Stats:

81% (01:34) correct 19% (01:25) wrong based on 109 sessions

HideShow timer Statistics

During an experiment, the growth rate of a bacteria colony is recorded. It is found that, to a good approximation, the growth rate of the number of bacteria in the colony is given by

\(R=\sqrt{N}(2000-(20-T)^2)\),

where R is the growth rate in millions per hour, N is the number of bacteria, in millions, at the beginning of the experiment, and T is the time, in minutes, that had passed since the beginning of the experiment. The experiment is 1 hour long, so T varies between zero and 60. What is the maximum growth rate of the bacteria colony recorded during the experiment?

A. 400√N millions of bacteria per hour
B. √N millions of bacteria per hour
C. 2000 millions of bacteria per hour
D. 2000√N millions of bacteria per hour
E. 1600 millions of bacteria per hour

Originally posted by goodyear2013 on 27 Aug 2014, 04:34.
Last edited by Bunuel on 27 Aug 2014, 05:02, edited 1 time in total.
Edited the question.
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 50002
Re: During an experiment, the growth rate of a bacteria colony  [#permalink]

Show Tags

New post 27 Aug 2014, 05:06
1
goodyear2013 wrote:
During an experiment, the growth rate of a bacteria colony is recorded. It is found that, to a good approximation, the growth rate of the number of bacteria in the colony is given by

\(R=\sqrt{N}(2000-(20-T)^2)\),

where R is the growth rate in millions per hour, N is the number of bacteria, in millions, at the beginning of the experiment, and T is the time, in minutes, that had passed since the beginning of the experiment. The experiment is 1 hour long, so T varies between zero and 60. What is the maximum growth rate of the bacteria colony recorded during the experiment?

A. 400√N millions of bacteria per hour
B. √N millions of bacteria per hour
C. 2000 millions of bacteria per hour
D. 2000√N millions of bacteria per hour
E. 1600 millions of bacteria per hour


Given that \(R=\sqrt{N}(2000-(20-T)^2)\).

To maximize R we need to maximize (2000-(20-T)^2).
To maximize (2000-(20-T)^2) we need to minimize (20-T)^2 (the value subtracted from 2000).
The minimum value of (20-T)^2 is 0 for T = 20.

Therefore, the maximum value of R is \(R=\sqrt{N}(2000-0)=2000\sqrt{N}\).

Answer: D.

Hope it's clear.
_________________

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

Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 8459
Premium Member
Re: During an experiment, the growth rate of a bacteria colony  [#permalink]

Show Tags

New post 03 Oct 2018, 10:23
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

GMAT Club Bot
Re: During an experiment, the growth rate of a bacteria colony &nbs [#permalink] 03 Oct 2018, 10:23
Display posts from previous: Sort by

During an experiment, the growth rate of a bacteria colony

  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®.