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

It is currently 20 Sep 2018, 00:09

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

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

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

Hide Tags

Manager
Manager
avatar
Joined: 29 Nov 2011
Posts: 78
Standing on the origin of an xy-coordinate plane, John takes  [#permalink]

Show Tags

New post 13 Feb 2012, 22:36
9
00:00
A
B
C
D
E

Difficulty:

  95% (hard)

Question Stats:

46% (02:20) correct 54% (02:23) wrong based on 130 sessions

HideShow timer Statistics

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
Most Helpful Expert Reply
Veritas Prep GMAT Instructor
User avatar
P
Joined: 16 Oct 2010
Posts: 8281
Location: Pune, India
Re: Probability PS  [#permalink]

Show Tags

New post 14 Feb 2012, 01:25
13
2
Smita04 wrote:
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


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

Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >

GMAT self-study has never been more personalized or more fun. Try ORION Free!

Most Helpful Community Reply
Manager
Manager
User avatar
Status: Employed
Joined: 17 Nov 2011
Posts: 88
Location: Pakistan
Concentration: International Business, Marketing
GMAT 1: 720 Q49 V40
GPA: 3.2
WE: Business Development (Internet and New Media)
Re: Probability PS  [#permalink]

Show Tags

New post 13 Feb 2012, 23:18
7
1
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
routes.jpg [ 90.8 KiB | Viewed 3209 times ]


Hence B
_________________

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

General Discussion
Retired Moderator
avatar
B
Joined: 17 Sep 2013
Posts: 361
Concentration: Strategy, General Management
GMAT 1: 730 Q51 V38
WE: Analyst (Consulting)
GMAT ToolKit User Premium Member Reviews Badge
Re: Standing on the origin of an xy-coordinate plane, John takes  [#permalink]

Show Tags

New post 21 May 2014, 00:57
1
It took me about 3.5 mins to solve...I forgot some cases initially

Total no of cases=4^4
Way 1- 1 each of L,R,U,D- They can be arranged in 4! ways..4!
Way 2- 2 each of R & L..RRLL- They can be arranged in 4!/2!*2!= 6
Way 2- 2 each of D & U..DDUU- They can be arranged in 4!/2!*2!= 6

36 ways possible/4*4*4*4
=9/64

I think it helps to think directions as numbers with opposite signs...In this case the sum of the 4 numbers should be 0
_________________

Appreciate the efforts...KUDOS for all
Don't let an extra chromosome get you down..:P

Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 8097
Premium Member
Re: Standing on the origin of an xy-coordinate plane, John takes  [#permalink]

Show Tags

New post 17 May 2017, 13:28
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: Standing on the origin of an xy-coordinate plane, John takes &nbs [#permalink] 17 May 2017, 13:28
Display posts from previous: Sort by

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

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

Events & Promotions

PREV
NEXT


cron

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®.