The CSCS Exam – Math Questions (Answer)

Posted by on Jul 24, 2014 in Exam Preparation, Practice Questions | 1 comment

See my previous post for background. Note that I did edit that post on 6/21.

The question is:

The collegiate training center is currently undergoing renovations and all 6 teams of 124 athletes need to share a smaller facility. You modify the facility arrangement to fit slightly more power racks – for a total of 7. The athletic director insists on every athlete maintaining their 1 hour of strength training. The training center is open 8 hours, but every athlete is pairing up and sharing racks operating at a 1:1 work:rest ratio. However, since you are using power racks assume that racking and re-racking weights will cause a 15% drop in efficiency in rack use.
The athletic director asks if you figured out a plan for the athletes, what do you tell him?
 
I. We can’t accommodate the athletes
II. We can accommodate the athletes
III. We need the facility open 1 more hour
IV. We need the facility open 4 more hours
 
A. II only
B. I only
C. II and III
D. II and IV
 

In questions like these, I like to think of it in terms of needs and resources

Needs

By needs I simply mean how many resources are required to get the task done. We have 6 teams and 124 athletes, but in this case we aren’t given any scheduling or segregation requirements between the teams – so the number 6 is irrelevant. Each athlete requires 1 hour of strength training, but will be pairing up and operating at 1:1 work:rest ratio. So in terms of time at the station they will only really need 30 minutes. However due to the 15% loss in efficiency due to racking and re-racking weights, each athlete will need closer to 35minutes. Multiply this number by 124 athletes and you get the total number of rack-minutes you need.

 

What my scratch paper might look like on exam day

Resources

The training center is open 8 hours, with 7 racks.

8 hours x 60min/1hour x 7 racks = 3360 rack-minutes. Notice again I like to keep descriptive “made up” units to describe the resources available. Rack-minutes are a resource just like any material resource that we use math to describe (8 six packs x 6beers/six pack = 48 beers, etc).

A quick comparison of our needs vs resources reveals 4340 – 3360 = 980 that we are still in need of 980 minutes of platform-minutes. If we look at the possible answers to the question, we can go back and calculate which option yields us the best answer.

1 additional hour gets us 1 hour x 60min x 7 stations = 420 minutes
4 additional hours gets us another 1680 minutes

resources

More scribbles

See from the math that we really only need 980 extra minutes, somewhere between 2 and 3 hours. However since 3 hours isn’t an option, the correct answer is the one that BEST meets the objectives in question – 1 hour isn’t enough, and even though 4 hours is overkill – it’s the only answer that meets our needs. So the answer is D.

We can accommodate the athletes and
We need the facility open an additional four hours

One Comment

  1. Can you explain me the 1:1 work:rest = 30 min ?

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