Re: Math question from the GRE General Test
- From: israel@xxxxxxxxxxx (Robert Israel)
- Date: 23 Nov 2005 17:43:54 GMT
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
.
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