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Manager  Joined: 18 Jun 2004
Posts: 82
Location: san jose , CA
A rectangular yard is 20 yards wide and 40 yards long, it is  [#permalink]

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4
15 00:00

Difficulty:   95% (hard)

Question Stats: 39% (03:26) correct 61% (03:11) wrong based on 557 sessions

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A rectangular yard is 20 yards wide and 40 yards long. It is surrounded by a thick hedge that grows on the border of the property, but completely within the boundaries of the yard. If the hedge covers an area of 171 square yards, what is the width?

A. 160/120
B. 171/120
C. 180/120
D. 191/120
E. 800/120

Originally posted by rahul on 29 Jul 2004, 13:59.
Last edited by Bunuel on 07 Apr 2012, 05:17, edited 1 time in total.
Edited the question
Math Expert V
Joined: 02 Sep 2009
Posts: 60646
Re: A rectangular yard is 20 yards wide and 40 yards long, it is  [#permalink]

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9
6
ikokurin wrote:
I am not sure why you subtract 2n instead of just 1n from each side? And, is there a way to show what is happening graphically please? If possible please go over this moment in detail. Thanks a lot.

Welcome to GMAT Club. Below is an answer to your question with a diagram.

A rectangular yard is 20 yards wide and 40 yards long. It is surrounded by a thick hedge that grows on the border of the property, but completely within the boundaries of the yard. If the hedge covers an area of 171 square yards, what is the width?
A. 160/120
B. 171/120
C. 180/120
D. 191/120
E. 800/120
Attachment: Garden.png [ 3.94 KiB | Viewed 13432 times ]

The area of the whole yard is 20*40=800 square yards;
The area of the uncovered yard is 800-171=629 square yards (the whole area minus the area of the portion of the yard which is covered by the hedge);

Now, the width of the uncovered yard is 20-2x and the length is 40-2x, so its area is (20-2x)(40-2x)=629 --> (20-2x)(40-2x)=17*37. At this point it's better to substitute the values from answer choices rather than to solve for x. Answer choice C, 3/2 fits.

P.S. Not a good question overall because of its poor wording.
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##### General Discussion
Director  Joined: 16 Jun 2004
Posts: 688

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I think the area of hedge is wrong - 171^2 is larger than the yard area. Pls clarify.
Manager  Joined: 18 Jun 2004
Posts: 82
Location: san jose , CA

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venksune wrote:
I think the area of hedge is wrong - 171^2 is larger than the yard area. Pls clarify.

It's not square of 171 but 171 square yards , area of hedge is 171
CEO  Joined: 07 Jul 2004
Posts: 3181
Location: Singapore

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3
Let n be the width of the hedge and assuming it grows uniformly

the 40(20) - (40-2n)(20-2n) = 171

4n^2 - 120n +171 = 0

Solving for n gives 1.5 or 28.5

From the choices, (C) is 1.5.
No choices gave n as 28.5, so (C) is the answer.
Senior Manager  Joined: 07 Oct 2003
Posts: 268
Location: Manhattan

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1
ywilfred wrote:
Let n be the width of the hedge and assuming it grows uniformly

the 40(20) - (40-2n)(20-2n) = 171

4n^2 - 120n +171 = 0

Solving for n gives 1.5 or 28.5

From the choices, (C) is 1.5.
No choices gave n as 28.5, so (C) is the answer.

can we really be expected to solve this type of equation for gmat??
CEO  Joined: 07 Jul 2004
Posts: 3181
Location: Singapore

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Frankly, I'm not sure. I am going for my first GMAT probably in November or Decemer. But nothing beats going through problems and getting a hang of hard and tough questiosn before going for the actual test. You'll find yourself feeling better before you step into the test centre !
Intern  Joined: 06 Apr 2012
Posts: 30
Re: A rectangular yard is 20 yards wide and 40 yards long, it is  [#permalink]

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I am not sure why you subtract 2n instead of just 1n from each side? And, is there a way to show what is happening graphically please? If possible please go over this moment in detail. Thanks a lot.
Manager  B
Joined: 10 Mar 2014
Posts: 177
Re: A rectangular yard is 20 yards wide and 40 yards long, it is  [#permalink]

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Bunuel wrote:
ikokurin wrote:
I am not sure why you subtract 2n instead of just 1n from each side? And, is there a way to show what is happening graphically please? If possible please go over this moment in detail. Thanks a lot.

Welcome to GMAT Club. Below is an answer to your question with a diagram.

A rectangular yard is 20 yards wide and 40 yards long. It is surrounded by a thick hedge that grows on the border of the property, but completely within the boundaries of the yard. If the hedge covers an area of 171 square yards, what is the width?
A. 160/120
B. 171/120
C. 180/120
D. 191/120
E. 800/120
Attachment:
Garden.png

The area of the whole yard is 20*40=800 square yards;
The area of the uncovered yard is 800-171=629 square yards (the whole area minus the area of the portion of the yard which is covered by the hedge);

Now, the width of the uncovered yard is 20-2x and the length is 40-2x, so its area is (20-2x)(40-2x)=629 --> (20-2x)(40-2x)=17*37. At this point it's better to substitute the values from answer choices rather than to solve for x. Answer choice C, 3/2 fits.

P.S. Not a good question overall because of its poor wording.

Thanks bunnel. Really good and clear explaination
Intern  Joined: 26 Mar 2014
Posts: 2
Re: A rectangular yard is 20 yards wide and 40 yards long, it is  [#permalink]

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800-171 = 629
629 = (40-2x)(20-2x)
629 =800 - 80x - 40x + 4x^2
629 = 800 = 120x + 4x^2
120x-4x^2 = 171
x = 1.5
Intern  Joined: 29 Mar 2014
Posts: 12
Location: United States
Concentration: Entrepreneurship, Finance
GMAT 1: 720 Q50 V39
GPA: 3

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ywilfred wrote:
Let n be the width of the hedge and assuming it grows uniformly

the 40(20) - (40-2n)(20-2n) = 171

4n^2 - 120n +171 = 0

Solving for n gives 1.5 or 28.5

From the choices, (C) is 1.5.
No choices gave n as 28.5, so (C) is the answer.

This is the right approach.. however n cannot be 28.5 because the width of the entire area is just 20 yards, so the only answer is 1.5
Manager  Joined: 28 Apr 2014
Posts: 189
Re: A rectangular yard is 20 yards wide and 40 yards long, it is  [#permalink]

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Bunuel wrote:
ikokurin wrote:
I am not sure why you subtract 2n instead of just 1n from each side? And, is there a way to show what is happening graphically please? If possible please go over this moment in detail. Thanks a lot.

Welcome to GMAT Club. Below is an answer to your question with a diagram.

A rectangular yard is 20 yards wide and 40 yards long. It is surrounded by a thick hedge that grows on the border of the property, but completely within the boundaries of the yard. If the hedge covers an area of 171 square yards, what is the width?
A. 160/120
B. 171/120
C. 180/120
D. 191/120
E. 800/120
Attachment:
Garden.png

The area of the whole yard is 20*40=800 square yards;
The area of the uncovered yard is 800-171=629 square yards (the whole area minus the area of the portion of the yard which is covered by the hedge);

Now, the width of the uncovered yard is 20-2x and the length is 40-2x, so its area is (20-2x)(40-2x)=629 --> (20-2x)(40-2x)=17*37. At this point it's better to substitute the values from answer choices rather than to solve for x. Answer choice C, 3/2 fits.

P.S. Not a good question overall because of its poor wording.

Bunuel I have a doubt .

Can't this hedge be treated as a rectangle of length = perimeter of original rectangle i.e. 120yard . Then width will be equal to Area / length = 171/120.

Something like a close strip of paper which can be cut and extended to make a big band
Math Expert V
Joined: 02 Sep 2009
Posts: 60646
Re: A rectangular yard is 20 yards wide and 40 yards long, it is  [#permalink]

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himanshujovi wrote:
Bunuel wrote:
ikokurin wrote:
I am not sure why you subtract 2n instead of just 1n from each side? And, is there a way to show what is happening graphically please? If possible please go over this moment in detail. Thanks a lot.

Welcome to GMAT Club. Below is an answer to your question with a diagram.

A rectangular yard is 20 yards wide and 40 yards long. It is surrounded by a thick hedge that grows on the border of the property, but completely within the boundaries of the yard. If the hedge covers an area of 171 square yards, what is the width?
A. 160/120
B. 171/120
C. 180/120
D. 191/120
E. 800/120 The area of the whole yard is 20*40=800 square yards;
The area of the uncovered yard is 800-171=629 square yards (the whole area minus the area of the portion of the yard which is covered by the hedge);

Now, the width of the uncovered yard is 20-2x and the length is 40-2x, so its area is (20-2x)(40-2x)=629 --> (20-2x)(40-2x)=17*37. At this point it's better to substitute the values from answer choices rather than to solve for x. Answer choice C, 3/2 fits.

P.S. Not a good question overall because of its poor wording.

Bunuel I have a doubt .

Can't this hedge be treated as a rectangle of length = perimeter of original rectangle i.e. 120yard . Then width will be equal to Area / length = 171/120.

Something like a close strip of paper which can be cut and extended to make a big band

How can the hedge have the length of 120 yards if it is entirely within the boundaries of the yard?
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Manager  Joined: 28 Apr 2014
Posts: 189
Re: A rectangular yard is 20 yards wide and 40 yards long, it is  [#permalink]

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Let me try and explain. If we cut at each vertex , the closed figure can turn into a big ,thin strip with length being equal to perimeter and width same as before. The area will remain same as before.
Math Expert V
Joined: 02 Sep 2009
Posts: 60646
Re: A rectangular yard is 20 yards wide and 40 yards long, it is  [#permalink]

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himanshujovi wrote:
Let me try and explain. If we cut at each vertex , the closed figure can turn into a big ,thin strip with length being equal to perimeter and width same as before. The area will remain same as before.

We are told that the rectangular yard is 20 yards wide and 40 yards long. Why are you changing the dimensions of the yard? If you mean something elese please upload the figure.
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Senior Manager  Joined: 15 Oct 2015
Posts: 297
Concentration: Finance, Strategy
GPA: 3.93
WE: Account Management (Education)
Re: A rectangular yard is 20 yards wide and 40 yards long, it is  [#permalink]

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rahul wrote:
A rectangular yard is 20 yards wide and 40 yards long. It is surrounded by a thick hedge that grows on the border of the property, but completely within the boundaries of the yard. If the hedge covers an area of 171 square yards, what is the width?

A. 160/120
B. 171/120
C. 180/120
D. 191/120
E. 800/120

My mind couldn't go into this question. each option(width) produced lenght that is longer than that of the field whcih is supposed to be larger than. Any mistake in this question? Some one even suggested that they mean 171 (sqaured) yards. thats even more preposterous as 171squared is larger than 800. Can someone explain what the question is talking about first?
Math Expert V
Joined: 02 Aug 2009
Posts: 8336
Re: A rectangular yard is 20 yards wide and 40 yards long, it is  [#permalink]

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Nez wrote:
rahul wrote:
A rectangular yard is 20 yards wide and 40 yards long. It is surrounded by a thick hedge that grows on the border of the property, but completely within the boundaries of the yard. If the hedge covers an area of 171 square yards, what is the width?

A. 160/120
B. 171/120
C. 180/120
D. 191/120
E. 800/120

My mind couldn't go into this question. each option(width) produced lenght that is longer than that of the field whcih is supposed to be larger than. Any mistake in this question? Some one even suggested that they mean 171 (sqaured) yards. thats even more preposterous as 171squared is larger than 800. Can someone explain what the question is talking about first?

Hi Nez,

the width is 160/120 which is nearly 1.5 yards.. so its OK..
what 171 square yards means is that 171 is the area of width in square yards..
same as if unit of length is in m, the area can be in square m...
171 sq yards means only 171 and not 171^2..
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Math Expert V
Joined: 02 Aug 2009
Posts: 8336
Re: A rectangular yard is 20 yards wide and 40 yards long, it is  [#permalink]

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rahul wrote:
A rectangular yard is 20 yards wide and 40 yards long. It is surrounded by a thick hedge that grows on the border of the property, but completely within the boundaries of the yard. If the hedge covers an area of 171 square yards, what is the width?

A. 160/120
B. 171/120
C. 180/120
D. 191/120
E. 800/120

Hi,
Another method where you can make use of choices given to home on to correct choice..

lets imagine the strip be x yards all along the perimeter..
so Area= perimeter*x - four corners of x*x

A= 2(20+40)x-4x^2=171..
120x-4x^2=171..

two ways hereafter:-

1) substitute ways and find answer

2)since all choices are in fraction with denominator 120, lets take x=y/120, where y is an integer..
now 120x will be an integer and 171 is an integer so 4x^2 will also be an integer (since Integer-Integer=Integer)..
4x^2=4*y^2/120^2= (y/60)^2 should be an integer ..
so y or the NUMERATOR should be a multiple of 60..
only 180 in C is multiple of 60..so ans is C

_________________ Re: A rectangular yard is 20 yards wide and 40 yards long, it is   [#permalink] 24 Feb 2016, 23:08
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