NEW HERE? LEARN MORE
closeclose
Last visit was: 24 Apr 2024, 08:24 It is currently 24 Apr 2024, 08:24
Decision Tracker
My Rewards
New posts
New comers' posts

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.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel

James and Henry are at the northwest corner of their busines

SORT BY:
Date
Kudos
Tags:
Find Similar Topics 
Show Tags
Hide Tags
User avatar
gmatbull
Senior Manager
Senior Manager
Joined: 21 Dec 2009
Posts: 337
Own Kudos [?]: 2443 [7]
Given Kudos: 20
Concentration: Entrepreneurship, Finance
Send PM
James and Henry are at the northwest corner of their busines [#permalink] New post   13 Nov 2012, 04:22
7
Bookmarks
00:00
A
B
C
D
E

Difficulty:

95% (hard)

Question Stats:

49% (03:29) correct 51% (03:17) wrong based on 98 sessions
Hide Show timer Statistics
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
ShowHide Answer
Official Answer
B
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92902
Own Kudos [?]: 618754 [4]
Given Kudos: 81587
Send PM
CAT Tests Forum Quiz Mode
Re: James and Henry are at the northwest corner of their busines [#permalink] New post   13 Nov 2012, 04:52
2
Kudos
2
Bookmarks
Expert Reply
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
Football field.png [ 5.69 KiB | Viewed 4871 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.

Answer: B.
User avatar
gmatbull
Senior Manager
Senior Manager
Joined: 21 Dec 2009
Posts: 337
Own Kudos [?]: 2443 [1]
Given Kudos: 20
Concentration: Entrepreneurship, Finance
Send PM
Re: James and Henry are at the northwest corner of their busines [#permalink] New post   14 Nov 2012, 00:52
1
Kudos
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.
avatar
rashmilagisetty
Intern
Intern
Joined: 07 Jun 2012
Posts: 1
Own Kudos [?]: 1 [1]
Given Kudos: 5
Send PM
Re: James and Henry are at the northwest corner of their busines [#permalink] New post   17 Nov 2012, 13:04
1
Kudos
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.
User avatar
gmatbull
Senior Manager
Senior Manager
Joined: 21 Dec 2009
Posts: 337
Own Kudos [?]: 2443 [1]
Given Kudos: 20
Concentration: Entrepreneurship, Finance
Send PM
Re: James and Henry are at the northwest corner of their busines [#permalink] New post   18 Nov 2012, 00:22
1
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
james n Henry.jpg [ 8.93 KiB | Viewed 4643 times ]

User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92902
Own Kudos [?]: 618754 [0]
Given Kudos: 81587
Send PM
CAT Tests Forum Quiz Mode
Re: James and Henry are at the northwest corner of their busines [#permalink] New post   25 Aug 2013, 06:37
Expert Reply
Bumping for review and further discussion.
User avatar
Infinitive
Intern
Intern
Joined: 30 Nov 2013
Posts: 15
Own Kudos [?]: 10 [0]
Given Kudos: 20
Concentration: Strategy, General Management
Schools: Krannert '17
Send PM
GMAT ToolKit User Reviews Badge
Re: James and Henry are at the northwest corner of their busines [#permalink] New post   30 Nov 2013, 11:14
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.
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92902
Own Kudos [?]: 618754 [1]
Given Kudos: 81587
Send PM
CAT Tests Forum Quiz Mode
Re: James and Henry are at the northwest corner of their busines [#permalink] New post   05 Dec 2013, 08:00
1
Kudos
Expert Reply
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.
avatar
np1986
Intern
Intern
Joined: 05 Dec 2013
Posts: 2
Own Kudos [?]: [0]
Given Kudos: 1
Concentration: Strategy, Healthcare
Schools: Desautels '16
Send PM
Re: James and Henry are at the northwest corner of their busines [#permalink] New post   05 Dec 2013, 21:40
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?
User avatar
L
KarishmaB
Tutor
Joined: 16 Oct 2010
Posts: 14817
Own Kudos [?]: 64895 [3]
Given Kudos: 426
Location: Pune, India
Send PM
Re: James and Henry are at the northwest corner of their busines [#permalink] New post   05 Dec 2013, 21:59
2
Kudos
1
Bookmarks
Expert Reply
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.

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?


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)
User avatar
L
KarishmaB
Tutor
Joined: 16 Oct 2010
Posts: 14817
Own Kudos [?]: 64895 [0]
Given Kudos: 426
Location: Pune, India
Send PM
Re: James and Henry are at the northwest corner of their busines [#permalink] New post   05 Dec 2013, 23:54
Expert Reply
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.
avatar
np1986
Intern
Intern
Joined: 05 Dec 2013
Posts: 2
Own Kudos [?]: [0]
Given Kudos: 1
Concentration: Strategy, Healthcare
Schools: Desautels '16
Send PM
Re: James and Henry are at the northwest corner of their busines [#permalink] New post   09 Dec 2013, 20:04
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.
User avatar
L
Fdambro294
VP
VP
Joined: 10 Jul 2019
Posts: 1392
Own Kudos [?]: 542 [0]
Given Kudos: 1656
Send PM
Re: James and Henry are at the northwest corner of their busines [#permalink] New post   14 Nov 2020, 23:39
if you draw the picture correctly,

James walks the Hypotenuse of a Right Triangle with Legs of 300 and 160

Leg 1 = 8 *(20) = 160

Leg 2 = 15 * (20) = 300

This is a Pythagorean Triplet ----> 8 - 15 - 17

James will walk = 17 * (20) = 340


Henry will walk 180 vertically down.

Then he will walk the Hypotenuse of a Right Triangle with Legs of 120 and 160

This is another Pythagorean Triplet: 3 - 4 - 5

Leg 1 = 3 * (40) = 120

Leg 2 = 4 *(40) = 160

Hypotenuse = 5 * (40) = 200

Henry walks a Total of = 180 + 200 = 380


Henry walks 40 more than James -----> 380 - 340 = 40

-B-
GMAT Club Bot
gmatclubot
Re: James and Henry are at the northwest corner of their busines [#permalink]
14 Nov 2020, 23:39
Moderators:
Bunuel
Math Expert
92902 posts
yashikaaggarwal
Senior Moderator - Masters Forum
3137 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne
Main navigation
GMAT Resources
Partners
MBA Resources
www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions