It is currently 22 Feb 2018, 08:58

# TODAY:

MIT Sloan Releasing 1st Wave of Interview Invites - Join GMATClub CHAT for Live Updates

### 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

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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

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

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 43866
Peter and Jacob are at the northwest corner of a field, which is a rec [#permalink]

### Show Tags

15 Apr 2015, 03:49
Expert's post
4
This post was
BOOKMARKED
00:00

Difficulty:

95% (hard)

Question Stats:

38% (03:16) correct 62% (03:15) wrong based on 79 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.
[Reveal] Spoiler: OA

_________________
Retired Moderator
Status: On a mountain of skulls, in the castle of pain, I sit on a throne of blood.
Joined: 30 Jul 2013
Posts: 359
Re: Peter and Jacob are at the northwest corner of a field, which is a rec [#permalink]

### Show Tags

15 Apr 2015, 07:51
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

Manager
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

15 Apr 2015, 13:37
1
KUDOS
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
Manager
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

17 Apr 2015, 02:03
1
KUDOS
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.
Math Expert
Joined: 02 Sep 2009
Posts: 43866
Re: Peter and Jacob are at the northwest corner of a field, which is a rec [#permalink]

### Show Tags

20 Apr 2015, 05:06
1
KUDOS
Expert's post
1
This post was
BOOKMARKED
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 [ 9.54 KiB | Viewed 958 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 [ 10.63 KiB | Viewed 958 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)
_________________
Non-Human User
Joined: 09 Sep 2013
Posts: 13800
Re: Peter and Jacob are at the northwest corner of a field, which is a rec [#permalink]

### Show Tags

17 Feb 2017, 21:37
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.
_________________
Re: Peter and Jacob are at the northwest corner of a field, which is a rec   [#permalink] 17 Feb 2017, 21:37
Display posts from previous: Sort by