Thursday, May 21, 2009

In his book 200% of Nothing, Dewdney comments on how stupid American students in 1982 had trouble with this problem:

An army bus holds 36 soldiers. If 1,128 soldiers are being bussed to their training site, how many buses are needed.

Apparently only 70% of American students were able to get as far as 1,128/36 = 31 1/3. Additionally, however, only a third of those students when on to get the correct answer: 32, 'cause you can't have a third of a bus, right?


When taking a test, you have to ignore all quibbles caused by sloppy and inexact problem descriptions. Why can't we just use one bus and have it go back and forth repeatedly? Because it's a division problem. The solution is to do the division and stop. Maybe the buses can go back and forth, or maybe there's no time and you need concurrent transportation. The problem doesn't say, so you just do that math You lack the contextual knowledge to nitpick.

Dewdney is accurate that a third of a bus doesn't drive, but there's a big difference between using one third of a bus' capacity for your soldiers and filling the entire bus with soldiers. Suppose we also have two-thirds bus capacity of training equipment to ship? If you assess the soldiers themselves to require 32 buses, you end up procuring a total of 33 buses for them and their equipment. You shouldn't be assume that is the case or that it isn't, because you're taking a math test answering a division problem. Don't change your answer to mesh with unestablished context.

('Three to be safe.' -- George Frankly)

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