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

It is currently 23 Jun 2018, 18:37

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

Events & Promotions in June
Open Detailed Calendar

M05-18

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

Hide Tags

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 46297
M05-18 [#permalink]

Show Tags

New post 16 Sep 2014, 00:25
00:00
A
B
C
D
E

Difficulty:

  5% (low)

Question Stats:

79% (00:31) correct 21% (00:40) wrong based on 178 sessions

HideShow timer Statistics

To build a rectangular chicken pen, Mike has 40 meters of netting. If Mike wants to maximize the area of the pen, what will be the most favorable dimensions?

A. 12 x 8
B. 15 x 8
C. 10 x 10
D. 15 x 15
E. 15 x 5

_________________

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

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 46297
Re M05-18 [#permalink]

Show Tags

New post 16 Sep 2014, 00:25
Official Solution:

To build a rectangular chicken pen, Mike has 40 meters of netting. If Mike wants to maximize the area of the pen, what will be the most favorable dimensions?

A. 12 x 8
B. 15 x 8
C. 10 x 10
D. 15 x 15
E. 15 x 5


Approach 1:

Say the length and the width of the rectangle are \(x\) and \(y\).

Given: \(\text{Perimeter}=2x+2y=40\). Reduce by 2: \(x+y=20\). We have to maximize the area, so maximize the value of \(xy\).

Useful property: for given sum of two numbers, their product is maximized when they are equal. Hence, the value of \(xy\) will be maximized for \(x=y=10\).

Approach 2:

This question can be easily solved if one knows the following property: a square has a larger area than any other quadrilateral with the same perimeter.

So, in order to maximize the area our rectangle must be a square: \(\text{Perimeter}=4x=40\). Therefore \(x=10\).


Answer: C
_________________

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

Intern
Intern
avatar
Joined: 05 Aug 2015
Posts: 46
M05-18 [#permalink]

Show Tags

New post 13 Mar 2016, 00:12
Bunuel wrote:
Official Solution:

To build a rectangular chicken pen, Mike has 40 meters of netting. If Mike wants to maximize the area of the pen, what will be the most favorable dimensions?

A. 12 x 8
B. 15 x 8
C. 10 x 10
D. 15 x 15
E. 15 x 5


Approach 1:

Say the length and the width of the rectangle are \(x\) and \(y\).

Given: \(\text{Perimeter}=2x+2y=40\). Reduce by 2: \(x+y=20\). We have to maximize the area, so maximize the value of \(xy\).

Useful property: for given sum of two numbers, their product is maximized when they are equal. Hence, the value of \(xy\) will be maximized for \(x=y=10\).

Approach 2:

This question can be easily solved if one knows the following property: a square has a larger area than any other quadrilateral with the same perimeter.

So, in order to maximize the area our rectangle must be a square: \(\text{Perimeter}=4x=40\). Therefore \(x=10\).


Answer: C


Isn't this problem flawed? The prompt specifically asks for a RECTANGULAR pen, so I excluded C and D b/c they are SQUARE pens??

Edit: OK, so Square is a special kind of Rectangle. Keeping this post as this is an important subtle point here for this problem.
_________________

Working towards 25 Kudos for the Gmatclub Exams - help meee I'm poooor

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 46297
Re: M05-18 [#permalink]

Show Tags

New post 13 Mar 2016, 08:17
happyface101 wrote:
Bunuel wrote:
Official Solution:

To build a rectangular chicken pen, Mike has 40 meters of netting. If Mike wants to maximize the area of the pen, what will be the most favorable dimensions?

A. 12 x 8
B. 15 x 8
C. 10 x 10
D. 15 x 15
E. 15 x 5


Approach 1:

Say the length and the width of the rectangle are \(x\) and \(y\).

Given: \(\text{Perimeter}=2x+2y=40\). Reduce by 2: \(x+y=20\). We have to maximize the area, so maximize the value of \(xy\).

Useful property: for given sum of two numbers, their product is maximized when they are equal. Hence, the value of \(xy\) will be maximized for \(x=y=10\).

Approach 2:

This question can be easily solved if one knows the following property: a square has a larger area than any other quadrilateral with the same perimeter.

So, in order to maximize the area our rectangle must be a square: \(\text{Perimeter}=4x=40\). Therefore \(x=10\).


Answer: C


Isn't this problem flawed? The prompt specifically asks for a RECTANGULAR pen, so I excluded C and D b/c they are SQUARE pens??

Edit: OK, so Square is a special kind of Rectangle. Keeping this post as this is an important subtle point here for this problem.


Yes, every square is a rectangle but not vise-versa.
_________________

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

Intern
Intern
avatar
B
Joined: 26 Dec 2016
Posts: 20
Re: M05-18 [#permalink]

Show Tags

New post 28 Feb 2017, 06:59
Hi Bunuel,

it's may a stupid question, but how could you build a rectangle with the dimension 15x15 if you have only 40m netting ?


Thanks
SC Moderator
avatar
D
Joined: 22 May 2016
Posts: 1764
Premium Member CAT Tests
M05-18 [#permalink]

Show Tags

New post 25 Apr 2017, 05:58
BoomHH wrote:
Hi Bunuel,

it's may a stupid question, but how could you build a rectangle with the dimension 15x15 if you have only 40m netting ?

Thanks

IMO, not a dumb question, though you missed answer B's similar impossibility :-).

My VERY non-expert guess is that "15x15" is designed to hijack the person who, per Bunuel 's second explanation, correctly deploys "max area is square" but then, without tracking on actual numbers, incorrectly decides that if a square is good, a bigger square is better.
_________________

In the depths of winter, I finally learned
that within me there lay an invincible summer.

-- Albert Camus, "Return to Tipasa"

M05-18   [#permalink] 25 Apr 2017, 05:58
Display posts from previous: Sort by

M05-18

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

Moderators: chetan2u, Bunuel



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®.