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# James and Henry are at the northwest corner of their busines

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Director
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James and Henry are at the northwest corner of their busines [#permalink]  13 Nov 2012, 03:22
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Question Stats:

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James and Henry are at the northwest corner of their business school’s football field, which is a rectangle 300 ft long and 160 ft wide. James walks in a straight line directly to the southeast corner of the field. If Henry walks 180 ft down the west side of the field and then walks in a straight line directly to the southeast corner of the field, how many feet farther, to the nearest 10 ft, will Henry walk than James?

A. 20
B. 40
C. 80
D. 120
E. 140
[Reveal] Spoiler: OA

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Math Expert
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Re: James and Henry are at the northwest corner of their busines [#permalink]  13 Nov 2012, 03:52
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Expert's post
gmatbull wrote:
James and Henry are at the northwest corner of their business school’s football field, which is a rectangle 300 ft long and 160 ft wide. James walks in a straight line directly to the southeast corner of the field. If Henry walks 180 ft down the west side of the field and then walks in a straight line directly to the southeast corner of the field, how many feet farther, to the nearest 10 ft, will Henry walk than James?

A. 20
B. 40
C. 80
D. 120
E. 140

Look at the diagram below:
Attachment:

Football field.png [ 5.69 KiB | Viewed 1781 times ]
The distance covered by James (AD) is shown in blue and it equals to \sqrt{300^2+160^2}=\sqrt{10^2(30^2+16^2)}=10*\sqrt{1156}=340;

The distance covered by Henry (AB+BD) is shown in red and it equals to 180+\sqrt{120^2+160^2}=180+\sqrt{10^2(12^2+16)^2}=180+10\sqrt{400}=380;

The difference is 380-340=40.

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Re: James and Henry are at the northwest corner of their busines [#permalink]  13 Nov 2012, 23:52
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Thanks Bunuel for your lucid explanations as usual.
I misinterpreted the text below:
"If Henry walks 180 ft down the west side of the field " to mean
"Henry walks 180 ft westwards"; Sure, that was a misleading interpretation.

Actually, Henry walked DOWNWARD, but on the western wing of the field.
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Re: James and Henry are at the northwest corner of their busines [#permalink]  17 Nov 2012, 12:04
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How do we decide the rectangle layout to be? I took 300 to be the length from northeast to east whereas in the explanation it takes 160 for the same length.
Director
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Posts: 589
Concentration: Entrepreneurship, Finance
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Kudos [?]: 292 [1] , given: 20

Re: James and Henry are at the northwest corner of their busines [#permalink]  17 Nov 2012, 23:22
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KUDOS
rashmilagisetty wrote:
How do we decide the rectangle layout to be? I took 300 to be the length from
northeast to east whereas in the explanation it takes 160 for the same length.

Which ever orientation u prefer doesn't change the fact that it remains a rectangle as shown in the attached.
However, note that If Henry walks 180 ft down the west side of the field, the
vertical side must be the side with 300 ft.
Attachments

james n Henry.jpg [ 8.93 KiB | Viewed 1588 times ]

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Math Expert
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Re: James and Henry are at the northwest corner of their busines [#permalink]  05 Dec 2013, 07:00
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Expert's post
Infinitive wrote:
So what does this sentence mean please?

James and Henry are at the northwest corner of their business school’s football field, which is a rectangle 300 ft long and 160 ft wide. James walks in a straight line directly to the southeast corner of the field. If Henry walks 180 ft down the west side of the field and then walks in a straight line directly to the southeast corner of the field, how many feet farther, to the nearest 10 ft, will Henry walk than James?

A. 20
B. 40
C. 80
D. 120
E. 140

This is the only sentence that put me off that I didnt understand.

I guess the question intends us to do some approximations to get the correct answer but as you can see we can get the exact answer quite easily, thus approximation is not necessary.
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Re: James and Henry are at the northwest corner of their busines [#permalink]  05 Dec 2013, 20:59
1
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Expert's post
np1986 wrote:
Bunuel wrote:
gmatbull wrote:
James and Henry are at the northwest corner of their business school’s football field, which is a rectangle 300 ft long and 160 ft wide. James walks in a straight line directly to the southeast corner of the field. If Henry walks 180 ft down the west side of the field and then walks in a straight line directly to the southeast corner of the field, how many feet farther, to the nearest 10 ft, will Henry walk than James?

A. 20
B. 40
C. 80
D. 120
E. 140

Look at the diagram below:
Attachment:
Football field.png
The distance covered by James (AD) is shown in blue and it equals to \sqrt{300^2+160^2}=\sqrt{10^2(30^2+16^2)}=10*\sqrt{1156}=340;

The distance covered by Henry (AB+BD) is shown in red and it equals to 180+\sqrt{120^2+160^2}=180+\sqrt{10^2(12^2+16)^2}=180+10\sqrt{400}=380;

The difference is 380-340=40.

Is there an alternative (and quicker) way to get the solution without doing the calculations, e.g. through ballparking and eliminating answer options?

Actually, the method shown by Bunuel is quite straight forward and you don't need to do any calculations if you just remember some of your pythagorean triplets (and that's why we suggest you to remember them!)

BC = 120, CD = 160
BC:CD = 3:4
Does it remind you of 3-4-5 triplet?
120 is 3*40 and 160 is 4*40 so BD will be 5*40 = 200
So Henry traveled 180 + 200 = 380

AB = 160, BD = 300
So AB:BD = 8:15
Remember 8-15-17? (the third triplet after 3-4-5 and 5-12-13)
Hence AD should be 17*20 = 340
James traveled 340

Difference = 40

I have seen the following triplets coming in handy:
( 3, 4, 5 ) ( 5, 12, 13) ( 8, 15, 17) ( 7, 24, 25)
(20, 21, 29) and ( 9, 40, 41)
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Save $100 on Veritas Prep GMAT Courses And Admissions Consulting Enroll now. Pay later. Take advantage of Veritas Prep's flexible payment plan options. Veritas Prep Reviews Math Expert Joined: 02 Sep 2009 Posts: 23422 Followers: 3614 Kudos [?]: 28951 [0], given: 2874 Re: James and Henry are at the northwest corner of their busines [#permalink] 25 Aug 2013, 05:37 Expert's post Bumping for review and further discussion. _________________ Intern Joined: 30 Nov 2013 Posts: 3 GMAT Date: 12-31-2013 Followers: 0 Kudos [?]: 0 [0], given: 10 Re: James and Henry are at the northwest corner of their busines [#permalink] 30 Nov 2013, 10:14 So what does this sentence mean please? James and Henry are at the northwest corner of their business school’s football field, which is a rectangle 300 ft long and 160 ft wide. James walks in a straight line directly to the southeast corner of the field. If Henry walks 180 ft down the west side of the field and then walks in a straight line directly to the southeast corner of the field, how many feet farther, to the nearest 10 ft, will Henry walk than James? A. 20 B. 40 C. 80 D. 120 E. 140 This is the only sentence that put me off that I didnt understand. Intern Joined: 05 Dec 2013 Posts: 2 Concentration: Strategy, Healthcare Schools: Desautels '16 Followers: 0 Kudos [?]: 0 [0], given: 1 Re: James and Henry are at the northwest corner of their busines [#permalink] 05 Dec 2013, 20:40 Bunuel wrote: gmatbull wrote: James and Henry are at the northwest corner of their business school’s football field, which is a rectangle 300 ft long and 160 ft wide. James walks in a straight line directly to the southeast corner of the field. If Henry walks 180 ft down the west side of the field and then walks in a straight line directly to the southeast corner of the field, how many feet farther, to the nearest 10 ft, will Henry walk than James? A. 20 B. 40 C. 80 D. 120 E. 140 Look at the diagram below: Attachment: Football field.png The distance covered by James (AD) is shown in blue and it equals to \sqrt{300^2+160^2}=\sqrt{10^2(30^2+16^2)}=10*\sqrt{1156}=340; The distance covered by Henry (AB+BD) is shown in red and it equals to 180+\sqrt{120^2+160^2}=180+\sqrt{10^2(12^2+16)^2}=180+10\sqrt{400}=380; The difference is 380-340=40. Answer: B. Is there an alternative (and quicker) way to get the solution without doing the calculations, e.g. through ballparking and eliminating answer options? Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 4877 Location: Pune, India Followers: 1157 Kudos [?]: 5381 [0], given: 165 Re: James and Henry are at the northwest corner of their busines [#permalink] 05 Dec 2013, 22:54 Expert's post rashmilagisetty wrote: How do we decide the rectangle layout to be? I took 300 to be the length from northeast to east whereas in the explanation it takes 160 for the same length. That is a valid concern. Note that there are two definitions of length: 1. Length is the longest side of the rectangle. 2. Width is from side to side and length is whatever isn't width (i.e. the side from up to down in a rectangle) (this definition is less embraced than the first one) If the side from up to down is the longest side, then there is no conflict. Keeping this in mind, when drawing the figure, given that length is the longer of the two, I would make the diagram as shown by Bunuel and there will be no conflict. _________________ Karishma Veritas Prep | GMAT Instructor My Blog Save$100 on Veritas Prep GMAT Courses And Admissions Consulting
Enroll now. Pay later. Take advantage of Veritas Prep's flexible payment plan options.

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Schools: Desautels '16
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Re: James and Henry are at the northwest corner of their busines [#permalink]  09 Dec 2013, 19:04
VeritasPrepKarishma wrote:
np1986 wrote:
Is there an alternative (and quicker) way to get the solution without doing the calculations, e.g. through ballparking and eliminating answer options?

Actually, the method shown by Bunuel is quite straight forward and you don't need to do any calculations if you just remember some of your pythagorean triplets (and that's why we suggest you to remember them!)

BC = 120, CD = 160
BC:CD = 3:4
Does it remind you of 3-4-5 triplet?
120 is 3*40 and 160 is 4*40 so BD will be 5*40 = 200
So Henry traveled 180 + 200 = 380

AB = 160, BD = 300
So AB:BD = 8:15
Remember 8-15-17? (the third triplet after 3-4-5 and 5-12-13)
Hence AD should be 17*20 = 340
James traveled 340

Difference = 40

I have seen the following triplets coming in handy:
( 3, 4, 5 ) ( 5, 12, 13) ( 8, 15, 17) ( 7, 24, 25)
(20, 21, 29) and ( 9, 40, 41)

Thanks! This is quite helpful and should make the calculations much easier.
Re: James and Henry are at the northwest corner of their busines   [#permalink] 09 Dec 2013, 19:04
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