May 24 10:00 PM PDT  11:00 PM PDT Join a FREE 1day workshop and learn how to ace the GMAT while keeping your fulltime job. Limited for the first 99 registrants. May 25 07:00 AM PDT  09:00 AM PDT Attend this webinar and master GMAT SC in 10 days by learning how meaning and logic can help you tackle 700+ level SC questions with ease. May 27 01:00 AM PDT  11:59 PM PDT All GMAT Club Tests are free and open on May 27th for Memorial Day! May 27 10:00 PM PDT  11:00 PM PDT Special savings are here for Magoosh GMAT Prep! Even better  save 20% on the plan of your choice, now through midnight on Tuesday, 5/27
Author 
Message 
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 55266

Anna has to visit at least 2 European cities on her vacation trip. If
[#permalink]
Show Tags
13 May 2017, 14:05
Question Stats:
54% (01:48) correct 46% (01:35) wrong based on 196 sessions
HideShow timer Statistics
Anna has to visit at least 2 European cities on her vacation trip. If she can visit only London, Paris, Rome, or Madrid, how many different itineraries, defined as the sequence of visited cities, can Anna create? A. 12 B. 36 C. 48 D. 60 E. 72
Official Answer and Stats are available only to registered users. Register/ Login.
_________________



Retired Moderator
Status: Long way to go!
Joined: 10 Oct 2016
Posts: 1353
Location: Viet Nam

Re: Anna has to visit at least 2 European cities on her vacation trip. If
[#permalink]
Show Tags
13 May 2017, 20:43
Bunuel wrote: Anna has to visit at least 2 European cities on her vacation trip. If she can visit only London, Paris, Rome, or Madrid, how many different itineraries, defined as the sequence of visited cities, can Anna create?
A. 12 B. 36 C. 48 D. 60 E. 72 The question asks the different itineraries, and we need to count the order. For example, visiting city A first and visiting city B later is different from visiting city B first and visiting city A later. To visit 2 cities from 4 cities, there are \(4 \times 3 = 12\) different itineraries To visit 3 cities from 4 cities, there are \(4 \times 3 \times 2= 24\) different itineraries To visit 4 cities from 4 cities, there are \(4 \times 3 \times 2 \times 1= 24\) different itineraries The total different itineraries are \(12 + 24 + 24 =60\) different itineraries. The answer is D.
_________________



CEO
Status: GMATINSIGHT Tutor
Joined: 08 Jul 2010
Posts: 2931
Location: India
GMAT: INSIGHT
WE: Education (Education)

Anna has to visit at least 2 European cities on her vacation trip. If
[#permalink]
Show Tags
13 May 2017, 22:32
Bunuel wrote: Anna has to visit at least 2 European cities on her vacation trip. If she can visit only London, Paris, Rome, or Madrid, how many different itineraries, defined as the sequence of visited cities, can Anna create?
A. 12 B. 36 C. 48 D. 60 E. 72 Atleast 2 cities to be visited Case 1: Exactly 2 cities are first chosen and then itineraries are planned in = 4C2*2! ways = 6*2 = 12 waysCase 2: Exactly 3 cities are first chosen and then itineraries are planned in = 4C3*3! ways = 4*6 = 24 waysCase 3: Exactly 4 cities are first chosen and then itineraries are planned in = 4C4*4! ways = 1*24 = 24 waysTotal Ways to make itineraries = 12+24+24 = 60 ways Answer: option D
_________________
Prosper!!!GMATinsightBhoopendra Singh and Dr.Sushma Jha email: info@GMATinsight.com I Call us : +919999687183 / 9891333772 Online OneonOne Skype based classes and Classroom Coaching in South and West Delhihttp://www.GMATinsight.com/testimonials.htmlACCESS FREE GMAT TESTS HERE:22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION



SVP
Joined: 26 Mar 2013
Posts: 2176

Re: Anna has to visit at least 2 European cities on her vacation trip. If
[#permalink]
Show Tags
14 May 2017, 04:23
Bunuel wrote: Anna has to visit at least 2 European cities on her vacation trip. If she can visit only London, Paris, Rome, or Madrid, how many different itineraries, defined as the sequence of visited cities, can Anna create?
A. 12 B. 36 C. 48 D. 60 E. 72 I did it hard way. I tried to see a pattern for one city. I used London. Take all combination from London to Paris L  P L  P  R L  P  R M L  P  M R Take all combination from London to Paris L  R L  R  P L  R  P  M L  R  M  P Take all combination from London to Madrid L  M L  M  P L  M  P  R L  M  R  P Total ways for one city =12 ways Because we need to make for FOUR cities =12 * 4 =48 ways. I would like to know where i went wrong? Thanks in advance



SVP
Joined: 26 Mar 2013
Posts: 2176

Re: Anna has to visit at least 2 European cities on her vacation trip. If
[#permalink]
Show Tags
14 May 2017, 08:03
nguyendinhtuong wrote: Mo2men wrote: Bunuel wrote: Anna has to visit at least 2 European cities on her vacation trip. If she can visit only London, Paris, Rome, or Madrid, how many different itineraries, defined as the sequence of visited cities, can Anna create?
A. 12 B. 36 C. 48 D. 60 E. 72 I did it hard way. I tried to see a pattern for one city. I used London. Take all combination from London to Paris L  P L  P  R L  P  ML  P  R M L  P  M R Take all combination from London to Paris L  R L  R  P L  R  ML  R  P  M L  R  M  P Take all combination from London to Madrid L  M L  M  P L  M  RL  M  P  R L  M  R  P Total ways for one city =15 ways Because we need to make for FOUR cities =12 * 4 =48 ways. 15 * 4 = 60I would like to know where i went wrong? Thanks in advance I was searching for 15 ways but I could notice my problem. Thanks a lot for your help.



Current Student
Joined: 04 Jan 2016
Posts: 166
Location: United States (NY)
GMAT 1: 620 Q44 V32 GMAT 2: 600 Q48 V25 GMAT 3: 660 Q42 V39
GPA: 3.48

Re: Anna has to visit at least 2 European cities on her vacation trip. If
[#permalink]
Show Tags
14 May 2017, 13:53
The itinerary should be at least two, meaning the itinerary (x) is equal or bigger than 2. We have three different cases that we need to consider: two cities, three cities and all four cities.
two cities: 4*3= 12 three cities: 4*3*2= 24 and four cities: 4!=4*3*2=24
sum of three cases: 12+24+24= 60
The correct option: D



EMPOWERgmat Instructor
Status: GMAT Assassin/CoFounder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 14197
Location: United States (CA)

Re: Anna has to visit at least 2 European cities on her vacation trip. If
[#permalink]
Show Tags
14 May 2017, 15:22
Mo2men wrote: Bunuel wrote: Anna has to visit at least 2 European cities on her vacation trip. If she can visit only London, Paris, Rome, or Madrid, how many different itineraries, defined as the sequence of visited cities, can Anna create?
A. 12 B. 36 C. 48 D. 60 E. 72 I did it hard way. I tried to see a pattern for one city. I used London. Take all combination from London to Paris L  P L  P  R L  P  R M L  P  M R Take all combination from London to Paris L  R L  R  P L  R  P  M L  R  M  P Take all combination from London to Madrid L  M L  M  P L  M  P  R L  M  R  P Total ways for one city =12 ways Because we need to make for FOUR cities =12 * 4 =48 ways. I would like to know where i went wrong? Thanks in advance Hi Mo2men, Your approach CAN absolutely work here  but you have to make sure that you're considering ALL of the possibilities (and you missed a few). For example, in your first 'group' (involving London/Paris as the first two locations), you listed the following 4 options: L  P L  P  R L  P  R  M L  P  M  R However, you forgot one option... L  P  M You made this exact same error in each of your 3 examples, meaning that you missed 3 of the possibilities. If you include those 3 options along with the 12 that you already listed, then you'll have a total of 15  meaning that there will be (15)(4) = 60 total options (and you'll have the correct answer). GMAT assassins aren't born, they're made, Rich
_________________
760+: Learn What GMAT Assassins Do to Score at the Highest Levels Contact Rich at: Rich.C@empowergmat.com*****Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!*****
Rich Cohen
CoFounder & GMAT Assassin
Special Offer: Save $75 + GMAT Club Tests Free
Official GMAT Exam Packs + 70 Pt. Improvement Guarantee www.empowergmat.com/



SVP
Joined: 26 Mar 2013
Posts: 2176

Re: Anna has to visit at least 2 European cities on her vacation trip. If
[#permalink]
Show Tags
14 May 2017, 15:33
EMPOWERgmatRichC wrote: Hi Mo2men,
Your approach CAN absolutely work here  but you have to make sure that you're considering ALL of the possibilities (and you missed a few).
For example, in your first 'group' (involving London/Paris as the first two locations), you listed the following 4 options:
L  P L  P  R L  P  R  M L  P  M  R
However, you forgot one option...
L  P  M
You made this exact same error in each of your 3 examples, meaning that you missed 3 of the possibilities. If you include those 3 options along with the 12 that you already listed, then you'll have a total of 15  meaning that there will be (15)(4) = 60 total options (and you'll have the correct answer).
GMAT assassins aren't born, they're made, Rich Thanks Rich for your kind help and support.



Intern
Joined: 27 Nov 2016
Posts: 4

Re: Anna has to visit at least 2 European cities on her vacation trip. If
[#permalink]
Show Tags
15 May 2017, 23:55
Am I reading the question stem correctly ?
I am considering the cases where Anna travels to LPR + LPM not in Rome and Madrid included together, meaning if she travels Rome she can not include Madrid in her itinerary.



Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 6206
Location: United States (CA)

Re: Anna has to visit at least 2 European cities on her vacation trip. If
[#permalink]
Show Tags
07 Oct 2018, 19:25
Bunuel wrote: Anna has to visit at least 2 European cities on her vacation trip. If she can visit only London, Paris, Rome, or Madrid, how many different itineraries, defined as the sequence of visited cities, can Anna create?
A. 12 B. 36 C. 48 D. 60 E. 72 To visit at least 2 of the 4 given European cities is to visit 2, 3, or all 4 cities. Since each itinerary must be made up of a different sequence of cities, order is important and thus we have a permutation problem. Let’s determine the number of ways she can visit 2, 3, or all 4 cities. The number of ways she can visit exactly 2 cities is 4P2 = 4! / 2! = 4 x 3 = 12. The number of ways she can visit exactly 3 cities is 4P3 = 4! / 1! = 4 x 3 x 2 = 24. The number of ways she can visit all 4 cities is 4P4 = 4! / 0! = 4 x 3 x 2 x 1 = 24. (Recall that 0! = 1.) Thus, the total number of ways she can visit at least 2 of the 4 cities is 12 + 24 + 24 = 60. Answer: D
_________________
5star rated online GMAT quant self study course See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews If you find one of my posts helpful, please take a moment to click on the "Kudos" button.




Re: Anna has to visit at least 2 European cities on her vacation trip. If
[#permalink]
07 Oct 2018, 19:25






