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GMAT Diagnostic Test Question 36

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GMAT Diagnostic Test Question 36 [#permalink] New post 06 Jun 2009, 22:23
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GMAT Diagnostic Test Question 36
Field: geometry
Difficulty: 750

What is the approximate minimum length of a rope required to enclose an area of 154 square meters?

A. 154
B. 60
C. 57
D. 50
E. 44
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Last edited by bb on 29 Sep 2013, 20:41, edited 2 times in total.
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Re: GMAT Diagnostic Test Question 36 [#permalink] New post 10 Jun 2009, 19:10
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Explanation
Official Answer: E

Since a circle has the minimum possible perimeter for a given area, then in order to minimize the length of a rope it should enclose a circle.

So, 154 square meters should be the area of a circle: area=\pi{r^2}=154 --> approximate value of \pi is \frac{22}{7} --> \frac{22}{7}*{r^2}=154 --> r^2\approx{49} --> r\approx{7}.

The length of a rope will equal to the circumference of the circle: circumference=2\pi{r}\approx{2*\frac{22}{7}*7}=44.

Answer: E.
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Last edited by bb on 28 Sep 2013, 20:46, edited 1 time in total.
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Re: GMAT Diagnostic Test Question 36 [#permalink] New post 01 Oct 2012, 07:20
Expert's post
bb wrote:
GMAT Diagnostic Test Question 36
Field: geometry
Difficulty: 750
Rating:


If an x meter long rope can enclose (or cover) a maximum area of 50 square meters, what is the approximate length of the rope?

A. 4
B. 7
C. 10
D. 20
E. 25


BELOW IS REVISED VERSION OF THIS QUESTION:

What is the approximate minimum length of a rope required to enclose an area of 154 square meters.

A. 154
B. 60
C. 57
D. 50
E. 44

Since a circle has the minimum possible perimeter for a given area, then in order to minimize the length of a rope it should enclose a circle.

So, 154 square meters should be the area of a circle: area=\pi{r^2}=154 --> approximate value of \pi is \frac{22}{7} --> \frac{22}{7}*{r^2}=154 --> r^2\approx{49} --> r\approx{7}.

The length of a rope will equal to the circumference of the circle: circumference=2\pi{r}\approx{2*\frac{22}{7}*7}=44.

Answer: E.
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Re: GMAT Diagnostic Test Question 36 [#permalink] New post 16 Dec 2013, 01:14
bb wrote:
GMAT Diagnostic Test Question 36
Field: geometry
Difficulty: 750

What is the approximate minimum length of a rope required to enclose an area of 154 square meters?

A. 154
B. 60
C. 57
D. 50
E. 44


Dear bb,

I understand that Im just a beginner but this question well bellow 600 cause even I solved it in seconds.
just a friendly suggestion :wink:
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Re: GMAT Diagnostic Test Question 36 [#permalink] New post 18 Dec 2013, 06:09
How can we assume the area to be a circle? What if the area was a square?

Then A^2 = 154
Nearest perfect square to 154 is 144 which gives us A=12.5 (The actual value of A should be something between 12 and 13 so this 12.5 is only an approximate value)

Perimeter of a square = 4A = 4*12.5 = 50

Hence the approximate length of the rope should be 50.

Answer: D
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Re: GMAT Diagnostic Test Question 36 [#permalink] New post 18 Dec 2013, 06:13
Expert's post
aakrity wrote:
How can we assume the area to be a circle? What if the area was a square?

Then A^2 = 154
Nearest perfect square to 154 is 144 which gives us A=12.5 (The actual value of A should be something between 12 and 13 so this 12.5 is only an approximate value)

Perimeter of a square = 4A = 4*12.5 = 50

Hence the approximate length of the rope should be 50.

Answer: D


Please check this post: gmat-diagnostic-test-question-79366.html#p1126850

Hope it helps.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

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?
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Re: GMAT Diagnostic Test Question 36 [#permalink] New post 18 Dec 2013, 06:19
Bunuel wrote:
aakrity wrote:
How can we assume the area to be a circle? What if the area was a square?

Then A^2 = 154
Nearest perfect square to 154 is 144 which gives us A=12.5 (The actual value of A should be something between 12 and 13 so this 12.5 is only an approximate value)

Perimeter of a square = 4A = 4*12.5 = 50

Hence the approximate length of the rope should be 50.

Answer: D


Please check this post: gmat-diagnostic-test-question-79366.html#p1126850

Hope it helps.


Yes, the post helps. Thank you.
Re: GMAT Diagnostic Test Question 36   [#permalink] 18 Dec 2013, 06:19
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