What if an exercise wasn't uniquely defined?

[grzz]

TL;DR Summary

Points of view of examiner and student may not be coincident.

A math exam question asked for the ratio of two wheels given the required information about the number of revolutions made along a certain distance by the two wheels of a penny-farthing bike.

Some students gave the ratio of the radii while others gave the ratio of the areas.

What should an examiner do when confronted with these two types of answers?

Thanks for any help.

 

[etotheipi]

Accept them both, since it is the fault of the examiner for writing an ill-defined question!

 

[fresh_42]

Summary:: Points of view of examiner and student may not be coincident.

revolutions made along a certain distance

... indicates, that the ratio of the circumferences, i.e. of the radii is asked for. Nothing in the text points to areas.

 

[DaveC426913]

Fresh is right. Would ratios of volume or mass have to be accepted as well?

 

[etotheipi]

Volume and mass are different; you'd need to know the three-dimensional geometry of the wheel for the former as well as material properties for the latter. Meanwhile, area is a perfectly reasonable measure of 'size' of a two-dimensional region.

 

[fresh_42]

One can always find interpretations that are not intended if one only is willing to. E.g. one could solve for the ratio of angles, which are defined by all revolutions of the wheels along the given distance.

 

[Vanadium 50]

Isn't the "ratio of wheels" equal to 1? One front wheel and one back wheel.

 

[grzz]

I am inclined to be in favour with the reply of "etotheipi', though I totally missed the perfectly logical reply of 'Vanadium 50'!

Anyway, thanks for all contributions.