Standing on the origin of an xy-coordinate plane, John takes

Oldest

Best Reply

Author

Message

TAGS:

Manager

Joined: 29 Nov 2011

Posts: 83

Followers: 0

Kudos [?]: 8 [0], given: 37

Standing on the origin of an xy-coordinate plane, John takes [#permalink]

13 Feb 2012, 22:36

00:00

Question Stats:

50% (06:58) correct

50% (02:41) wrong

based on 0 sessions

Standing on the origin of an xy-coordinate plane, John takes a 1-unit step at random in one of the following 4 directions: up, down, left, or right. If he takes 3 more steps under the same random conditions, what is the probability that he winds up at the origin again?

(A) 7/64
(B) 9/64
(C) 11/64
(D) 13/64
(E) 15/64

Manager

Status: Employed

Joined: 17 Nov 2011

Posts: 101

Location: Pakistan

Concentration: International Business, Marketing

GMAT 1: 720 Q49 V40

GPA: 3.2

WE: Business Development (Internet and New Media)

Followers: 4

Kudos [?]: 42 [2] , given: 10

Re: Probability PS [#permalink]

13 Feb 2012, 23:18

This post received
KUDOS

This is the Manhattan Gmat Problem of the week this week. Extremely difficult to explain this without drawing. But lets suppose he takes a step in any one direction. Since he can take 4 different directions from there on in and he does this 3 times the total number of possibilities is 4*4*4=64

Now if you start drawing on a piece of paper, you will realise that there are 9 such possibilities where he can end up back on the origin so answer should be \frac{9}{64}. I am going to attach an image of all these possibilities along-with this post as well.

Attachment:

routes.jpg [ 90.8 KiB | Viewed 784 times ]

Hence B
_________________

"Nowadays, people know the price of everything, and the value of nothing." Oscar Wilde

Manager

Joined: 17 Sep 2011

Posts: 214

Followers: 0

Kudos [?]: 11 [0], given: 8

Re: Probability PS [#permalink]

14 Feb 2012, 00:35

The correct answer is B.
_________________

_________________
Giving +1 kudos is a better way of saying 'Thank You'.

Manager

Status: Employed

Joined: 17 Nov 2011

Posts: 101

Location: Pakistan

Concentration: International Business, Marketing

GMAT 1: 720 Q49 V40

GPA: 3.2

WE: Business Development (Internet and New Media)

Followers: 4

Kudos [?]: 42 [0], given: 10

Re: Probability PS [#permalink]

14 Feb 2012, 00:42

abhi47 wrote:

The correct answer is B.

What? No Kudos? .... I thought giving Kudos was the best way of saying thankyou :-D

_________________

"Nowadays, people know the price of everything, and the value of nothing." Oscar Wilde

Veritas Prep GMAT Instructor

Joined: 16 Oct 2010

Posts: 3113

Location: Pune, India

Followers: 572

Kudos [?]: 2014 [3] , given: 92

Re: Probability PS [#permalink]

14 Feb 2012, 01:25

This post received
KUDOS

Smita04 wrote:

Find the total number of possibilities first. He takes total 4 steps . He can take each step in any direction so there are a total of 4*4*4*4 possibilities (this includes UUUU, UDLR, DDLR etc etc)

He needs to be at the origin after 4 steps. So if he takes a step up, he needs to take a step down at some time. If he takes a step to the left, he needs to take one to the right at some time. Say if he takes two steps in this way - UL, his next two steps are defined - DR/RD. If instead, he takes two steps in this way - UU, his next two steps have to be DD.
There are two possibilities:
1. He goes only Up and Down or only Left and Right. UUDD can be arranged in 4!/(2!*2!) ways (includes UDUD, DUDU, DDUU etc). LLRR can also be arranged in 4!/(2!*2!) ways.
2. He goes Up/Down as well as Left/Right. UDLR can be arranged in 4! ways.

Total possible arrangements = 2*4!/(2!*2!) + 4!

Probability he comes back to the origin = (2*4!/(2!*2!) + 4!)/4*4*4*4 = 9/64
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Save 10% 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

Intern

Joined: 11 Jan 2012

Posts: 1

Followers: 0

Kudos [?]: 0 [0], given: 0

Re: Probability PS [#permalink]

14 Feb 2012, 01:27

thanks a lot omer. i was just trying to solve it but couldnt. wasnt getting 64 as denominator.

Manager

Joined: 29 Nov 2011

Posts: 83

Followers: 0

Kudos [?]: 8 [0], given: 37

Re: Standing on the origin of an xy-coordinate plane, John takes [#permalink]

14 Feb 2012, 05:08

Thanks Omer, you've explained it so clearly.

Re: Standing on the origin of an xy-coordinate plane, John takes [#permalink] 14 Feb 2012, 05:08

		Similar topics	Author	Replies	Last post
Similar Topics:		Coordinate plane_origin	IrinaOK	4	02 Sep 2007, 19:25
		In the xy-coordinate plane, line L and K intersect at the	jimjohn	1	26 Dec 2007, 20:03
	1	For any triangle in the xy-coordinate plane, the center of T	Capthan	2	12 Jun 2008, 12:23
	3	On the xy-coordinate plane, a quadrilateral is bounded by	fluke	13	17 May 2011, 04:07
		In the attached figure: On the xy-coordinate plane, a	nades09	2	24 Aug 2011, 20:25

Standing on the origin of an xy-coordinate plane, John takes

Main navigation

GMAT Resources

Partners

MBA Resources

GMAT ® is a registered trademark of the Graduate Management Admission Council ® (GMAC ®). GMAT Club's website has not been reviewed or endorsed by GMAC.