GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 18 Jun 2018, 15:50

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.

Close

Request Expert Reply

Confirm Cancel

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

Peter and Jacob are at the northwest corner of a field, which is a rec

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 46129
Peter and Jacob are at the northwest corner of a field, which is a rec [#permalink]

Show Tags

New post 15 Apr 2015, 04:49
00:00
A
B
C
D
E

Difficulty:

  95% (hard)

Question Stats:

39% (03:02) correct 61% (03:25) wrong based on 82 sessions

HideShow timer Statistics

Peter and Jacob are at the northwest corner of a field, which is a rectangle 300 ft long and 160 ft wide. Peter walks in a straight line directly to the southeast corner of the field. If Jacob 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, what is the difference in the distance traveled by the two?

(A) 20
(B) 40
(C) 80
(D) 120
(E) 140


Kudos for a correct solution.

_________________

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

Retired Moderator
avatar
B
Status: On a mountain of skulls, in the castle of pain, I sit on a throne of blood.
Joined: 30 Jul 2013
Posts: 351
GMAT ToolKit User Reviews Badge
Re: Peter and Jacob are at the northwest corner of a field, which is a rec [#permalink]

Show Tags

New post 15 Apr 2015, 08:51
Bunuel wrote:
Peter and Jacob are at the northwest corner of a field, which is a rectangle 300 ft long and 160 ft wide. Peter walks in a straight line directly to the southeast corner of the field. If Jacob 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, what is the difference in the distance traveled by the two?

(A) 20
(B) 40
(C) 80
(D) 120
(E) 140


Kudos for a correct solution.


Distance by Peter=Diagonal of the rectangle of 300*160 ft
\(\sqrt{90000+25600}\)
\(\sqrt{115600}\)
=340

Distance by Jacob = 180 + Diagonal of rectangle of 300*20 ft
=180 + \(\sqrt{90000+400}\)
=180+approx 300
=480 approx

Difference between the distance of Peter and Jacob = 480-340
=140

Answer: E
1 KUDOS received
Manager
Manager
avatar
Joined: 01 Jan 2015
Posts: 56
Re: Peter and Jacob are at the northwest corner of a field, which is a rec [#permalink]

Show Tags

New post 15 Apr 2015, 14:37
1
So Peter's distance = diagonal of the rectangle = sq root(300x300 + 160x160) = 340
Jacob's distance = 180+ sq root(120x120 + 160x160) = 180+200 = 380
Difference = 380-340 = 40
Answer B
1 KUDOS received
Manager
Manager
avatar
Joined: 18 Dec 2014
Posts: 100
Re: Peter and Jacob are at the northwest corner of a field, which is a rec [#permalink]

Show Tags

New post 17 Apr 2015, 03:03
1
Peter and Jacob are at the northwest corner of a field, which is a rectangle 300 ft long and 160 ft wide. Peter walks in a straight line directly to the southeast corner of the field. If Jacob 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, what is the difference in the distance traveled by the two?

(A) 20
(B) 40
(C) 80
(D) 120
(E) 140


Distance Peter:
300^2 + 160^2 = \sqrt{115600} -> 340

Distance Jacob:
120^2 + 160^2 = \sqrt{40000} -> 200
200 + 180 = 380

380 - 340 = 40. B.
Expert Post
1 KUDOS received
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 46129
Re: Peter and Jacob are at the northwest corner of a field, which is a rec [#permalink]

Show Tags

New post 20 Apr 2015, 06:06
1
1
Bunuel wrote:
Peter and Jacob are at the northwest corner of a field, which is a rectangle 300 ft long and 160 ft wide. Peter walks in a straight line directly to the southeast corner of the field. If Jacob 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, what is the difference in the distance traveled by the two?

(A) 20
(B) 40
(C) 80
(D) 120
(E) 140


Kudos for a correct solution.


VERITAS PREP OFFICIAL SOLUTION

The first thing we do in these “direction” questions is draw the diagram. But there is a problem here: how do we decide the orientation of the rectangle? It could be either of these two.
Attachment:
Ques5.jpg
Ques5.jpg [ 9.54 KiB | Viewed 1051 times ]

A few things help us decide this. 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 width isn’t (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, one could make the rectangle on the left and there will be no conflict. But the question maker may not want to take for granted that you know this.

So he/she leaves a clue – the question mentions that ‘Jacob walks 180 ft down the west side of the field’. There needs to be at least 180 ft on the west side of the field for him to travel that much. So the orientation on the left makes sense. This is something the question maker would have put to try to give you a hint of the orientation. Now that we know what our diagram should look like, we can proceed to solve this question.
Attachment:
Ques4.jpg
Ques4.jpg [ 10.63 KiB | Viewed 1051 times ]

If you just remember some of your pythagorean triplets, this question can be solved in moments (and that’s why we suggest you to remember them!) If not, it would involve some calculations.

QR = 160, RS = 300

So QR:RS = 8:15

Remember 8-15-17 pythagorean triplet? (the third triplet after 3-4-5 and 5-12-13)

Since the two sides are in the ratio 8:15, the hypotenuse must be 17. The common multiplier is 20 so QS should be 17*20 = 340

Therefore, Peter traveled 340 feet.

TP = 120, PS = 160

TP:PS = 3:4

Does it remind you of 3-4-5 triplet?

120 is 3*40 and 160 is 4*40 so TS will be 5*40 = 200

So Jacob traveled a total distance of 180 + 200 = 380 feet.

Difference between the distance traveled = 380 – 340 = 40 feet

Note: The following triplets come in handy: (3, 4, 5) (5, 12, 13) (8, 15, 17) (7, 24, 25) (20, 21, 29) and (9, 40, 41)
_________________

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

Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 6997
Premium Member
Re: Peter and Jacob are at the northwest corner of a field, which is a rec [#permalink]

Show Tags

New post 17 Feb 2017, 22:37
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

Re: Peter and Jacob are at the northwest corner of a field, which is a rec   [#permalink] 17 Feb 2017, 22:37
Display posts from previous: Sort by

Peter and Jacob are at the northwest corner of a field, which is a rec

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.