Q:

Does a word problem provide all information?

A while ago I asked a similar question about word problems and assumptions.
Is it a definition or an accepted-fact that word problems provide all information about the relevant existence/situation in the word problem?
Thanks to all!
EDIT, should've been clear. For example a problem like,
"A spherical balloon is inflated with gas at the
rate of 800 cubic centimeters per minute. How fast is the radius of the balloon increasing at the instant the radius is (a) 30 centimeters and (b) 60 centimeters?"

A:

$\S1$: A necessary clarification
It is simply a misunderstanding to think that while some math problems are "word problems", there are others that are not.  For example, any question posted to math.stackexchange.com that omitted words would probably be considered not to be a sufficiently clearly expressed question to remain open.  A list of problems in a textbook might look like this:

Find the following sums:
  $1$. ${}\qquad{} 13+28$
  $2$. ${}\qquad{} 97+42$
  $3$. ${}\qquad{} 58+19$
  ${}\  \vdots$
  ${}\  \vdots$
  ${}\  \vdots$
  $48$. ${}\qquad31+67$
  ${}\  \vdots$
  ${}\  \vdots$

A student looks at number $48$ and thinks it just says $31+67$, parses the "$+$" as a verb in the imperative mood telling him to find the sum, and concludes that it's not a "word problem" although the words "Find the following sums:" appear at the top.
If it says

$48$. ${}\qquad x^2-2x+35$

A student asking for help sometimes presents it as if it only says $x^2-2x+35$.  If the words at the top say "Factor the following polynomials" then it is quite a different problem from what it would be if it said "Differentiate the following functions of $x$."  But sometimes students posting to math.stackexchange.com write something like this: "How do I do this problem? $x^2-2x+35$?"  That's not really even a question: there is no question in the students mind about how to do something, where the student knows what it is that is to be done.  Obviously all this is a consequence of the fact that a duty is imposed upon students to learn mathematics.  Students who are there because mathematics is something they want to learn ask actual questions.
$\S2$: The heart of the answer:
Problems in mathematics books presume students know things before encountering the problem.  If a problem says "How big would the coefficient of friction have to be in order to prevent a car going along a horizontal road with radius of curvature 200 meters from skidding off the road while making the turn?" it would normally be presumed that the concept of coefficient of friction has been defined.
$\S3$: More examples
A student who was not a native speaker of English once asked me how I concluded that a certain number should be $12$.  It turned out he did not know the meaning of the word "dozen", which appeared in the statement of the problem.  So just what it is that a student is presumed to know might not be stated explicitly, but that kind of confusion is not what is normally intended.
The physicist Edwin Jaynes once stated a problem approximately as follows: "A very limp piece of string of length $L$ is thrown very unskillfully onto the floor.  Find the probability distribution of the distance between the two ends."  I think he actually intended the reader to know that he expected probability to be construed as logical epistemic probability rather than relative frequency.  But you had to know the context to see that!

