Oct 19 07:00 AM PDT  09:00 AM PDT Does GMAT RC seem like an uphill battle? eGMAT is conducting a free webinar to help you learn reading strategies that can enable you to solve 700+ level RC questions with at least 90% accuracy in less than 10 days. Sat., Oct 19th at 7 am PDT Oct 18 08:00 AM PDT  09:00 AM PDT Learn an intuitive, systematic approach that will maximize your success on Fillintheblank GMAT CR Questions. Oct 20 07:00 AM PDT  09:00 AM PDT Get personalized insights on how to achieve your Target Quant Score. Oct 22 08:00 PM PDT  09:00 PM PDT On Demand for $79. For a score of 4951 (from current actual score of 40+) AllInOne Standard & 700+ Level Questions (150 questions) Oct 23 08:00 AM PDT  09:00 AM PDT Join an exclusive interview with the people behind the test. If you're taking the GMAT, this is a webinar you cannot afford to miss!
Author 
Message 
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 58453

An auto assembly plant performs six functions with each frame that arr
[#permalink]
Show Tags
22 Apr 2015, 03:24
Question Stats:
43% (01:47) correct 57% (01:49) wrong based on 191 sessions
HideShow timer Statistics
An auto assembly plant performs six functions with each frame that arrives: add axles, add wheels to the axles, install the windshield to the frame, install the instrument panel, install the steering wheel, and install the interior seating. Once those six tasks are performed, each car goes to a separate building for finishing touches. If these tasks can be arranged along a linear assembly line in any order, except that the axles must be installed before the wheels can be added, how many ways can the assembly line be arranged? A. 120 B. 240 C. 360 D. 480 E. 720 Kudos for a correct solution.
Official Answer and Stats are available only to registered users. Register/ Login.
_________________




Current Student
Joined: 13 Nov 2014
Posts: 108

Re: An auto assembly plant performs six functions with each frame that arr
[#permalink]
Show Tags
22 Apr 2015, 11:13
C) 360 short way: there are 6C! ways to do the six tasks. Half will have wheels before axles and half will have axles before wheels. So we want 6C!/2 > 720/2 = 360
_________________
Gmat prep 1 600 Veritas 1 650 Veritas 2 680 Gmat prep 2 690 (48Q 37V) Gmat prep 5 730 (47Q 42V) Gmat prep 6 720 (48Q 41V)




Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 9706
Location: Pune, India

Re: An auto assembly plant performs six functions with each frame that arr
[#permalink]
Show Tags
23 Apr 2015, 06:02
For a discussion on the symmetry principle used to solve this question, check: http://www.veritasprep.com/blog/2011/10 ... spartii/
_________________
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 >



Manager
Joined: 27 Dec 2013
Posts: 199

Re: An auto assembly plant performs six functions with each frame that arr
[#permalink]
Show Tags
23 Apr 2015, 09:41
I like the Wofford09 answer but for a lengthy solution, here you go... If Axle can be first job, then rest five job can arranged in 5! ways. If the Axle is the second job, the Wheel can be done in 4 ways and the remaining 4 jobs can be arranged in 4!. If the Axle is the third job, the wheel can be done in 3 ways and the reamining 4 jobs can be arranged in 4!. If the Axle is the second job, the wheel can be done in 2 ways and the reamining 4 jobs can be arranged in 4!. ..... Finally total permuations.., 5! + (4+3+2+1) 4!= 360 ways. As soon as I saw the question, I started working on it.... I presume I have a slow a bit to be able to do what wooford09 Did. Bunuel wrote: An auto assembly plant performs six functions with each frame that arrives: add axles, add wheels to the axles, install the windshield to the frame, install the instrument panel, install the steering wheel, and install the interior seating. Once those six tasks are performed, each car goes to a separate building for finishing touches. If these tasks can be arranged along a linear assembly line in any order, except that the axles must be installed before the wheels can be added, how many ways can the assembly line be arranged?
A. 120 B. 240 C. 360 D. 480 E. 720
Kudos for a correct solution.
_________________
Kudos to you, for helping me with some KUDOS.



Current Student
Joined: 13 Nov 2014
Posts: 108

Re: An auto assembly plant performs six functions with each frame that arr
[#permalink]
Show Tags
23 Apr 2015, 09:51
shriramvelamuri wrote: I like the Wofford09 answer but for a lengthy solution, here you go... If Axle can be first job, then rest five job can arranged in 5! ways. If the Axle is the second job, the Wheel can be done in 4 ways and the remaining 4 jobs can be arranged in 4!. If the Axle is the third job, the wheel can be done in 3 ways and the reamining 4 jobs can be arranged in 4!. If the Axle is the second job, the wheel can be done in 2 ways and the reamining 4 jobs can be arranged in 4!. ..... Finally total permuations.., 5! + (4+3+2+1) 4!= 360 ways. As soon as I saw the question, I started working on it.... I presume I have a slow a bit to be able to do what wooford09 Did. Bunuel wrote: An auto assembly plant performs six functions with each frame that arrives: add axles, add wheels to the axles, install the windshield to the frame, install the instrument panel, install the steering wheel, and install the interior seating. Once those six tasks are performed, each car goes to a separate building for finishing touches. If these tasks can be arranged along a linear assembly line in any order, except that the axles must be installed before the wheels can be added, how many ways can the assembly line be arranged?
A. 120 B. 240 C. 360 D. 480 E. 720
Kudos for a correct solution. I think knowing the lengthy solution is also very important (and a very good exercise to do). Kudos
_________________
Gmat prep 1 600 Veritas 1 650 Veritas 2 680 Gmat prep 2 690 (48Q 37V) Gmat prep 5 730 (47Q 42V) Gmat prep 6 720 (48Q 41V)



Director
Joined: 21 May 2013
Posts: 636

Re: An auto assembly plant performs six functions with each frame that arr
[#permalink]
Show Tags
25 Apr 2015, 12:05
Bunuel wrote: An auto assembly plant performs six functions with each frame that arrives: add axles, add wheels to the axles, install the windshield to the frame, install the instrument panel, install the steering wheel, and install the interior seating. Once those six tasks are performed, each car goes to a separate building for finishing touches. If these tasks can be arranged along a linear assembly line in any order, except that the axles must be installed before the wheels can be added, how many ways can the assembly line be arranged?
A. 120 B. 240 C. 360 D. 480 E. 720
Kudos for a correct solution. Total number of ways in which the two specific functions can be selected out of the 6 functions=6C2 Remaining 4 functions can be arranged in 4! ways. Answer=6C2*4!=360 (C)



Math Expert
Joined: 02 Sep 2009
Posts: 58453

Re: An auto assembly plant performs six functions with each frame that arr
[#permalink]
Show Tags
27 Apr 2015, 04:03
Bunuel wrote: An auto assembly plant performs six functions with each frame that arrives: add axles, add wheels to the axles, install the windshield to the frame, install the instrument panel, install the steering wheel, and install the interior seating. Once those six tasks are performed, each car goes to a separate building for finishing touches. If these tasks can be arranged along a linear assembly line in any order, except that the axles must be installed before the wheels can be added, how many ways can the assembly line be arranged?
A. 120 B. 240 C. 360 D. 480 E. 720
Kudos for a correct solution. VERITAS PREP OFFICIAL SOLUTION:C. In this permutations problem (the order does matter  that's what they're asking about!), there are six items to be arranged in order, so the "unrestricted" permutation would be 6! = 720. But there's a catch  since wheels cannot come before axles, any permutation that would put wheels before axles does not work. How do you find that restriction? It's actually a bit simpler than you might think  if you're considering all possibilities, half the time axles will come before wheels (acceptable) and half the time wheels will come before axles (unacceptable). So take away the unacceptable half of the 720 arrangements and 360 are left.
_________________



Intern
Joined: 28 Oct 2015
Posts: 21

Re: An auto assembly plant performs six functions with each frame that arr
[#permalink]
Show Tags
30 Oct 2015, 07:12
Hi there,
I'm not able to quite see why is half before and half after. I understand it, but I can not see it!
Can anyone explain?
Thanks



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 9706
Location: Pune, India

Re: An auto assembly plant performs six functions with each frame that arr
[#permalink]
Show Tags
28 Nov 2016, 22:41
VeritasPrepKarishma wrote: For a discussion on the symmetry principle used to solve this question, check: http://www.veritasprep.com/blog/2011/10 ... spartii/Responding to a pm: Quote: Since there are 6 tasks and 2 of them have to performed in a specified order, I grouped them and we get a total of 5 tasks(group of 2 tasks acting as one) Then I arranged them to get total of 5! ways i.e 120 ways... Please tell me where I wrong...
Note that axles have to put before wheels but not necessarily immediately before. What I mean to say is that axles, wheels, windshield, instrument panel, steering wheel, interior seating is possible and so is axles, windshield, instrument panel, steering wheel, interior seating, wheels and also axles, windshield, instrument panel, wheels, steering wheel, interior seating etc The point is, as long as axles come sometime before wheels, it is fine. When you club them together in a group, you are only allowing case 1. That is the problem.
_________________
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: 07 Jan 2019
Posts: 10

Re: An auto assembly plant performs six functions with each frame that arr
[#permalink]
Show Tags
27 May 2019, 05:39
The mistake I did was taking A,W,_,_,_,_ . Now I took A,W as one block & rest others as separate blocks. This gives 5! as answer. But the logic we are missing is the question didn’t say both A,W should happen immediately after one another. It just said that W should happen after A.
So all the possible combinations are: A,W,_,_,_,_ A,W,_,_,_,_ A,W,_,_,_,_ A,W,_,_,_,_ A,W,_,_,_,_ _,A,W,_,_,_ _,A,_W,_,_ . . . . _,_,_,_,A,W
If Axle can be first job, then rest five job can arranged in 5! ways.
If the Axle is the second job, the Wheel can be done in 4 ways and the remaining 4 jobs can be arranged in 4!.
If the Axle is the third job, the wheel can be done in 3 ways and the reamining 4 jobs can be arranged in 4!.
If the Axle is the second job, the wheel can be done in 2 ways and the reamining 4 jobs can be arranged in 4!.
.....
Finally total permuations.., 5! + (4+3+2+1) 4!= 360 ways.
Posted from my mobile device



Intern
Joined: 19 Jul 2018
Posts: 13

Re: An auto assembly plant performs six functions with each frame that arr
[#permalink]
Show Tags
19 Aug 2019, 10:53
Total number of ways in which 6 functions can be arranged = 6! This will have only two types of scenarios involving installation of axles and fitting of wheels. 1. The former can happen before the latter. 2. The latter can happen before the former. In fact, the number of possible arrangements of both is equal to each other. Therefore, number of acceptable ways = 6!/2 = 360 ways.
_________________
Best Regards, Wizard of Oddz (Always do your best. What you plant now, you will harvest later.)



Manager
Joined: 30 May 2019
Posts: 63
Location: United States
Concentration: Technology, Strategy
GPA: 3.6

Re: An auto assembly plant performs six functions with each frame that arr
[#permalink]
Show Tags
04 Oct 2019, 13:43
KS15 wrote: Bunuel wrote: An auto assembly plant performs six functions with each frame that arrives: add axles, add wheels to the axles, install the windshield to the frame, install the instrument panel, install the steering wheel, and install the interior seating. Once those six tasks are performed, each car goes to a separate building for finishing touches. If these tasks can be arranged along a linear assembly line in any order, except that the axles must be installed before the wheels can be added, how many ways can the assembly line be arranged?
A. 120 B. 240 C. 360 D. 480 E. 720
Kudos for a correct solution. Total number of ways in which the two specific functions can be selected out of the 6 functions=6C2 Remaining 4 functions can be arranged in 4! ways. Answer=6C2*4!=360 (C) I see that this gives the answer but I don't understand why . Can you please explain why did you decide to choose 2 specific functions but not bother with arranging them as asked ?




Re: An auto assembly plant performs six functions with each frame that arr
[#permalink]
04 Oct 2019, 13:43






