Re: Math question from the GRE General Test

Robert Israel wrote:
> In article <3ujebdF11ipcoU1@xxxxxxxxxxxxxx>,
> Robert Low <mtx014@xxxxxxxxxxxxxx> wrote:
> >panayiotismanolakos@xxxxxxxxx wrote:
> >> Hi,
> >>
> >> The following question appears in the math section of a 'retired' GRE
> >> General Test. My claim is that the official answer is incorrect. Can
> >> someone provide feedback?
> >>
> >> It is given that y = x + (1/x) and 0 < x < 10. Is it true that (A) y >
> >> 100, (B) y < 100, (C) y = 100, or (D) there is not enough information
> >> to answer this question?
> >> My contention is that (B) is true while ETS contends that (D) is the
> >> case.
> >
> >If x=1, y=2, so A is not the case.
> >If x=0.0001, y=10000.0001, so B is not the case.
> >In neither of the above cases is y=100, so C is not the case.
> >Therefore none of A, B, or C is true for every x in
> >that range.
> >Since there is enough information to answer the question,
> >D is not the case.
> >
> >So the answer is 'none of the above'.
>
> There are a number of ambiguities here.
> The main problem is, what does "answer this question" mean?
> Which question? Would 'none of the above' constitute an answer?
> Would 'yes'? Is the author of the question claiming to have a
> particular x in mind that the question is about, or is s/he
> asking which, if any, of A, B, C is true for every x in the
> interval?
>
> As it stands, if "this question" is referring to the whole
> question, and "answer this question" means select one of the
> alternatives (A), (B), (C), (D), then this is a self-reference
> paradox.
> ETS's claim that (D) is the answer can't be right, because
> they are saying that there _is_ enough information here to
> select the answer (D). But that says that (D) is false.
> On the other hand, if you can't select (D), that says that
> (D) is true.
>
> Robert Israel israel@xxxxxxxxxxx
> Department of Mathematics http://www.math.ubc.ca/~israel
> University of British Columbia Vancouver, BC, Canada

I don't think so. Basically remove the letters from the question, the
answer is no. Were the answer to be yes, then the selection of the
choice, traditionally using the number two pencil on the scantron
***, with no mechanical or electronic computational aids allowed, is
basically compact shorthand for "yes, and the answer is this one of the
options."

If the question is phrased where more than one answer is correct, then
that is a bad question. Here, none of the options reflect a correct
resolution of the expressed query as to the range of the function f(x)
= x + 1/x for x on [0,10], i.e., resolve to tautology.

The "question" should read:

If y = x + 1/x, for x from zero to ten, indicate which of these applies
to y:

(a) y < 100
(b) y > 100
(c) y = 100
(d) none of the above

That is to say, it should be an imperative instead of a question.
There is the implicit "indicate your answer."

I don't know, it's been a long time since I took a college entrance
exam, I am not familiar with them, but that question is malformed.
Don't get me wrong I ace them. It's not a self-referential paradox,
the answer is no.

Ross

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