BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

Assembly line

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Master | Next Rank: 500 Posts
Posts: 113
Joined: Wed Dec 07, 2011 7:20 am
Thanked: 3 times

Assembly line

by manik11 » Thu Oct 29, 2015 7:29 am
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?

120

240

360

480

720

OA : C
Source : Veritas Prep

According to the official explanation half of the time wheels will come before axles and half of the time axles will come before wheels. I can't visualize this scenario.
Would really appreciate if the experts could break this down for me.
Top
Source: — Problem Solving |
User avatar
GMAT Instructor
Posts: 15539
Joined: Tue May 25, 2010 12:04 pm
Location: New York, NY
Thanked: 13060 times
Followed by:1906 members
GMAT Score:790

by GMATGuruNY » Thu Oct 29, 2015 7:36 am
Check my post here:

https://www.beatthegmat.com/six-mobsters ... 62073.html
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
Top
User avatar
Legendary Member
Posts: 2663
Joined: Wed Jan 14, 2015 8:25 am
Location: Boston, MA
Thanked: 1153 times
Followed by:128 members
GMAT Score:770

by DavidG@VeritasPrep » Thu Oct 29, 2015 7:47 am
According to the official explanation half of the time wheels will come before axles and half of the time axles will come before wheels. I can't visualize this scenario.
Would really appreciate if the experts could break this down for me.
Sometimes it's easier to conceptualize these issues with very simple scenarios. Imagine that attaching the wheels and attaching the axles are the only two procedures that need to be performed. Call attaching the wheels 'W' and call attaching the axles "A." So there are two sequences:

1) wheels first and then axles: WA
2) axles first and then wheels: AW

Clearly half the time wheels come first and half the time axles come first.

Now add one procedure, say, steering wheel. Call it S. Now there will be 3!, or 6 ways to arrange the procedures.

SAW
SWA
WSA
WAS
ASW
AWS

Notice that, again, half the time wheels come first (in red) and half the time axles come first. This makes sense. If there are two scenarios - either wheels must come first or axles must come first - then half the time it will be one scenario and half the time it will be the other.

That will always be true, no matter how many procedures are performed. So if we know that axles must come first, that will eliminate all the scenarios when wheels come first, or half of the total possibilities.
Veritas Prep | GMAT Instructor

Veritas Prep Reviews
Save $100 off any live Veritas Prep GMAT Course
Top
Post new topic Post Reply
• Page 1 of 1