Aug 20 08:00 PM PDT  09:00 PM PDT EMPOWERgmat is giving away the complete Official GMAT Exam Pack collection worth $100 with the 3 Month Pack ($299) Aug 20 09:00 PM PDT  10:00 PM PDT Take 20% off the plan of your choice, now through midnight on Tuesday, 8/20 Aug 22 09:00 PM PDT  10:00 PM PDT What you'll gain: Strategies and techniques for approaching featured GMAT topics, and much more. Thursday, August 22nd at 9 PM EDT Aug 24 07:00 AM PDT  09:00 AM PDT Learn reading strategies that can help even nonvoracious reader to master GMAT RC Aug 25 09:00 AM PDT  12:00 PM PDT Join a FREE 1day verbal workshop and learn how to ace the Verbal section with the best tips and strategies. Limited for the first 99 registrants. Register today! Aug 25 08:00 PM PDT  11:00 PM PDT Exclusive offer! Get 400+ Practice Questions, 25 Video lessons and 6+ Webinars for FREE.
Author 
Message 
TAGS:

Hide Tags

Senior Manager
Joined: 28 Dec 2010
Posts: 267
Location: India

An ant is clinging to one corner of a box in the shape of a
[#permalink]
Show Tags
28 Jun 2012, 18:58
Question Stats:
28% (02:19) correct 72% (02:06) wrong based on 343 sessions
HideShow timer Statistics
An ant is clinging to one corner of a box in the shape of a cube. The ant wants to get to the most distant corner of the box by crawling only along the edges of the cube and without ever revisiting a place it has been. How many different paths can the ant take to the most distant corner? A. 6 B. 12 C. 18 D. 24 E. 30
Official Answer and Stats are available only to registered users. Register/ Login.




Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 9541
Location: Pune, India

Re: Manhatta quant set 3
[#permalink]
Show Tags
28 Jun 2012, 23:42
vibhav wrote: An ant is clinging to one corner of a box in the shape of a cube. The ant wants to get to the most distant corner of the box by crawling only along the edges of the cube and without ever revisiting a place it has been. How many different paths can the ant take to the most distant corner?
A. 6 B.12 C.18 D.24 E.30 Make the cube and select two opposite corners. One where the ant is right now and the second is where it wants to reach. Notice that from its current position, it has 3 different paths that it can take i.e. it has 3 possible options. Make the ant move on any one path out of these 3. Once one path is chosen, it has two different paths it can take (it cannot take the third one since it cannot revisit the third point). Make the ant move on any one path out of these 2. Now, from this point, it again has 3 options to reach the point where it wanted to reach. Notice that the case will be the same even if you had selected different paths in the first two moves because it is a cube so all sides are the same. Total number of different paths = 3*2*3 = 18
_________________
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 >




Senior Manager
Joined: 17 Sep 2013
Posts: 324
Concentration: Strategy, General Management
WE: Analyst (Consulting)

Re: An ant is clinging to one corner of a box in the shape of a
[#permalink]
Show Tags
29 May 2014, 13:13
@ Bunuel I have to type it all over again coz u deleted my last post.. Here how does the ant have 3 choices after the second path..It again has 2 choices.. Also it misses all the complex paths that the ant visits not in 3 steps..say in 5 or 7 steps..(It is possible) Either I misunderstood the Q and the E or the explanation is incorrect I guess the way would be: No of ways to do in 3 steps: 3*2*1=6 5 steps: 3*2*1*1*1=6 7 steps: 3*2*1*1*1*1*1=6 No more steps are possible: total 18 ways Experts please comment
_________________
Appreciate the efforts...KUDOS for all Don't let an extra chromosome get you down..




Senior Manager
Joined: 28 Dec 2010
Posts: 267
Location: India

Re: Manhatta quant set 3
[#permalink]
Show Tags
28 Jun 2012, 18:59
guys any idea how this problem can be solved algebraically? the OE essentially sketches out the different paths, which will be very tedious on G day.



Manager
Joined: 20 Jul 2012
Posts: 115
Location: India
WE: Information Technology (Computer Software)

An ant is clinging to one corner of a box in the shape of a
[#permalink]
Show Tags
12 Jul 2014, 21:07
VeritasPrepKarishma wrote: vibhav wrote: An ant is clinging to one corner of a box in the shape of a cube. The ant wants to get to the most distant corner of the box by crawling only along the edges of the cube and without ever revisiting a place it has been. How many different paths can the ant take to the most distant corner?
A. 6 B.12 C.18 D.24 E.30 Make the cube and select two opposite corners. One where the ant is right now and the second is where it wants to reach. Notice that from its current position, it has 3 different paths that it can take i.e. it has 3 possible options. Make the ant move on any one path out of these 3. Once one path is chosen, it has two different paths it can take (it cannot take the third one since it cannot revisit the third point). Make the ant move on any one path out of these 2. Now, from this point, it again has 3 options to reach the point where it wanted to reach. Notice that the case will be the same even if you had selected different paths in the first two moves because it is a cube so all sides are the same. Total number of different paths = 3*2*3 = 18 Hi Karishma I could not get how there are three paths from the second point. Could you please explain in detail. Thanks



Senior Manager
Joined: 17 Sep 2013
Posts: 324
Concentration: Strategy, General Management
WE: Analyst (Consulting)

Re: An ant is clinging to one corner of a box in the shape of a
[#permalink]
Show Tags
16 Jul 2014, 12:55
JusTLucK04 wrote: @ Bunuel I have to type it all over again coz u deleted my last post.. Here how does the ant have 3 choices after the second path..It again has 2 choices.. Also it misses all the complex paths that the ant visits not in 3 steps..say in 5 or 7 steps..(It is possible) Either I misunderstood the Q and the E or the explanation is incorrect I guess the way would be: No of ways to do in 3 steps: 3*2*1=6 5 steps: 3*2*1*1*1=6 7 steps: 3*2*1*1*1*1*1=6 No more steps are possible: total 18 ways Experts please comment Bumping for review...Karishma & Bunuel..please review the solution in view of the above approach I have posted
_________________
Appreciate the efforts...KUDOS for all Don't let an extra chromosome get you down..



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 9541
Location: Pune, India

An ant is clinging to one corner of a box in the shape of a
[#permalink]
Show Tags
16 Jul 2014, 21:57
JusTLucK04 wrote: JusTLucK04 wrote: @ Bunuel I have to type it all over again coz u deleted my last post.. Here how does the ant have 3 choices after the second path..It again has 2 choices.. Also it misses all the complex paths that the ant visits not in 3 steps..say in 5 or 7 steps..(It is possible) Either I misunderstood the Q and the E or the explanation is incorrect I guess the way would be: No of ways to do in 3 steps: 3*2*1=6 5 steps: 3*2*1*1*1=6 7 steps: 3*2*1*1*1*1*1=6 No more steps are possible: total 18 ways Experts please comment Bumping for review...Karishma & Bunuel..please review the solution in view of the above approach I have posted Here is the reason the number of paths is 3*2*3 and how it takes everything into consideration: Attachment:
Ques3.jpg [ 6.31 KiB  Viewed 10808 times ]
I think the first two steps are clear so the first step is taken in 3 ways and second step in 2 ways. Now, draw the cube and see that the ant would be at one of three points (the points where you reach after traversing 2 edges)  E, C, G For each of these points, there are 3 unique ways in which the ant can reach the desired vertex. 1st way  Directly go to the desired point. If it is an E, this means EF 2nd way  Go via 3 edges e.g. if it came from AD DE, it goes EHHGGF 3rd way  Go via 5 edges e.g. if it came from AD DE, it goes EHHGGBBCCF Since it is a cube, we know that what works for one edge, will work for other two as well. So you multiply 3*2 by 3 to get 18.
_________________
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 >



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 9541
Location: Pune, India

An ant is clinging to one corner of a box in the shape of a
[#permalink]
Show Tags
16 Jul 2014, 22:00
JusTLucK04 wrote: JusTLucK04 wrote: @ Bunuel I have to type it all over again coz u deleted my last post.. Here how does the ant have 3 choices after the second path..It again has 2 choices.. Also it misses all the complex paths that the ant visits not in 3 steps..say in 5 or 7 steps..(It is possible) Either I misunderstood the Q and the E or the explanation is incorrect I guess the way would be: No of ways to do in 3 steps: 3*2*1=6 5 steps: 3*2*1*1*1=6 7 steps: 3*2*1*1*1*1*1=6 No more steps are possible: total 18 ways Experts please comment Bumping for review...Karishma & Bunuel..please review the solution in view of the above approach I have posted As for your solution, it is correct too, of course. You chose to split it into "number of paths used". But note the 1s you used in 5 steps and 7 steps. It means that paths are unique and the method involves some unnecessary counting. A cube gives us symmetry and it would be good to use that.
_________________
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 >



Intern
Joined: 11 Dec 2012
Posts: 25

Re: An ant is clinging to one corner of a box in the shape of a
[#permalink]
Show Tags
06 Sep 2015, 02:37
At first stage ant has three ways, right? At the second stage ant has only two ways, since it cannot return back on its path. At the third stage Ant has only one way to its destination. Henceforth, 3x2x1=6
Since there are three paths at the first stage we just need to add the outcomes of each three ways: 6+6+6=18



Senior Manager
Joined: 06 Jun 2016
Posts: 258
Location: India
Concentration: Operations, Strategy
GMAT 1: 600 Q49 V23 GMAT 2: 680 Q49 V34
GPA: 3.9

An ant is clinging to one corner of a box in the shape of a
[#permalink]
Show Tags
29 Oct 2016, 01:24
VeritasPrepKarishma wrote: JusTLucK04 wrote: JusTLucK04 wrote: Bunuel I have to type it all over again coz u deleted my last post.. Here how does the ant have 3 choices after the second path..It again has 2 choices.. Also it misses all the complex paths that the ant visits not in 3 steps..say in 5 or 7 steps..(It is possible) Either I misunderstood the Q and the E or the explanation is incorrect I guess the way would be: No of ways to do in 3 steps: 3*2*1=6 5 steps: 3*2*1*1*1=6 7 steps: 3*2*1*1*1*1*1=6 No more steps are possible: total 18 ways Experts please comment Bumping for review...Karishma & Bunuel..please review the solution in view of the above approach I have posted Here is the reason the number of paths is 3*2*3 and how it takes everything into consideration: Attachment: Ques3.jpg I think the first two steps are clear so the first step is taken in 3 ways and second step in 2 ways. Now, draw the cube and see that the ant would be at one of three points (the points where you reach after traversing 2 edges)  E, C, G For each of these points, there are 3 unique ways in which the ant can reach the desired vertex. 1st way  Directly go to the desired point. If it is an E, this means EF 2nd way  Go via 3 edges e.g. if it came from AD DE, it goes EHHGGF 3rd way  Go via 5 edges e.g. if it came from AD DE, it goes EHHGGBBCCF Since it is a cube, we know that what works for one edge, will work for other two as well. So you multiply 3*2 by 3 to get 18. VeritasPrepKarishma ma'am I still didn't understand the 3rd multiple of 3. Could you please explain it again? Considering the ant starts from E and its destination being B, From point E it has 3 distinct path. When it gets to point D,H or F it has 2 distinct path through which it can reach B. Now comes the third point. From D it can come to A or C, From H it can go to A or G and from F it can go to C or G again giving rise to 2 distinct path. Ma'am could you please explain from here?



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 9541
Location: Pune, India

Re: An ant is clinging to one corner of a box in the shape of a
[#permalink]
Show Tags
29 Oct 2016, 03:04
Vinayak Shenoy wrote: VeritasPrepKarishma ma'am I still didn't understand the 3rd multiple of 3. Could you please explain it again? Considering the ant starts from E and its destination being B, From point E it has 3 distinct path. When it gets to point D,H or F it has 2 distinct path through which it can reach B. Now comes the third point. From D it can come to A or C, From H it can go to A or G and from F it can go to C or G again giving rise to 2 distinct path. Ma'am could you please explain from here? I have discussed this question here: https://www.veritasprep.com/blog/2015/0 ... thegmat/See if it helps. Let me know if something is still unclear.
_________________
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 >



Intern
Joined: 02 Nov 2017
Posts: 2

Re: An ant is clinging to one corner of a box in the shape of a
[#permalink]
Show Tags
02 Nov 2017, 10:12
This question has a bit of IQ test feel to it. You need to be able to visualize the paths to fit the problem to a standard permutations/combinations calculation.
Sarah



Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 7399
Location: United States (CA)

Re: An ant is clinging to one corner of a box in the shape of a
[#permalink]
Show Tags
08 Jun 2018, 11:24
vibhav wrote: An ant is clinging to one corner of a box in the shape of a cube. The ant wants to get to the most distant corner of the box by crawling only along the edges of the cube and without ever revisiting a place it has been. How many different paths can the ant take to the most distant corner?
A. 6 B. 12 C. 18 D. 24 E. 30 Let’s say the ant is currently at corner A, thus it wants to go to corner G since it’s the furthest from A. Now from A, its next move is to B, to E, or to D. Let’s analyze the number of paths it can have if its next move is to B: ABFG ABFEHG ABFEHDCG ABCG ABCDHG ABCDHEFG We see that we have 6 paths if its first move is to B. Without listing the actual paths, if its first move is to E, there should be also 6 paths, and another 6 paths if its first move is to D. Therefore, there will be a total of 6 + 6 + 6 = 18 different paths from A to G. Answer: C
_________________
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.



Manager
Joined: 21 Jun 2019
Posts: 86
Location: Canada
Concentration: Finance, Accounting
GPA: 3.78

An ant is clinging to one corner of a box in the shape of a
[#permalink]
Show Tags
09 Jul 2019, 12:09
we have 12 edges and 6 faces in a cube, the ant got 12+6=18 ways answer is C
_________________
HIT KUDOS IF YOU FOUND ME HELPFUL !



Director
Joined: 19 Oct 2018
Posts: 772
Location: India

Re: An ant is clinging to one corner of a box in the shape of a
[#permalink]
Show Tags
09 Jul 2019, 15:45
Ant has to add 1 unit in x, y and z direction in order to reach to distant corner Case 1 (+1, +1, +1)= 3*2*1=6 Case 2 (+1, +1, 1, +1, +1)= 3*2*1*1*1=6 Case 3 (+1, +1, 1, +1, 1, +1, +1)= 3*2*1*1*1*1*1=6 Total number of ways = 6+6+6=18 vibhav wrote: An ant is clinging to one corner of a box in the shape of a cube. The ant wants to get to the most distant corner of the box by crawling only along the edges of the cube and without ever revisiting a place it has been. How many different paths can the ant take to the most distant corner?
A. 6 B. 12 C. 18 D. 24 E. 30



Intern
Joined: 08 Jun 2019
Posts: 1

Re: An ant is clinging to one corner of a box in the shape of a
[#permalink]
Show Tags
08 Aug 2019, 13:58
Different ways the ant can move is, 1. 3edges path(111) 2. 5edges path(113) 3. 7edges path(115)
Now, assuming that the ant doesn't feel adventurous and ventures back on the same path it crawled upon previously, Number of ways from Start Point (1) = 3(1 OR 1 OR 1) AND Number of ways from Mid Point (2) = 2(1 OR 1) AND Number of ways from Last Point (3) = 3(1 OR 1 OR 1)
Total ways = 3x2x3 = 18




Re: An ant is clinging to one corner of a box in the shape of a
[#permalink]
08 Aug 2019, 13:58






