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M05-18

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M05-18 [#permalink]

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New post 15 Sep 2014, 23:25
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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
[Reveal] Spoiler: OA

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Re M05-18 [#permalink]

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New post 15 Sep 2014, 23:25
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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
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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

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M05-18 [#permalink]

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New post 12 Mar 2016, 23:12
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.
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Re: M05-18 [#permalink]

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New post 13 Mar 2016, 07:17
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

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

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New post 28 Feb 2017, 05:59
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 ?


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M05-18 [#permalink]

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New post 25 Apr 2017, 04:58
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.
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M05-18   [#permalink] 25 Apr 2017, 04:58
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