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Re: a few more general GRE math problems

Subject: Re: a few more general GRE math problems
From:
Date: 31 Dec 2006 06:25:46 -0800
Newsgroups: sci.math
john wrote:
...


> Q2:
>   x > 1
>   y > 1
>
> What is greater?  1 / ( 1/x + 1/y)  or 1/x + 1/y     that is...
>
> a.                                   b.
>          1                                 1            1
> -------------------          or          -------  +   ------
>    1         1                             x           y
> -------  + ------
>    x         y
>
>
>
> A2: Need more information to determine the relationship.
>
>
> I got this one wrong after plugging in x = 2, y = 3
>
> so i figured....
>
> a.   xy                      b.   y + x
>    ----------                       ----------
>     x + y                           xy
>
>        6/5            >            5/6
>
> or if x= 2, y = 5
>
> then
>          10/7         >         7/10
>
>
> or if x = 5, y = 5
>
> then    25/10      >      10/25
>
> I can't get why you need more info to determine the relantionship..
> What's the trick here?
>

...

For reasons of time, I'd like to just comment on the question above.
You had exactly the right idea -- plug in simple values of x and y to
investigate.  The simpler, the better, therefore you should have
investigated the simplest case of all: x = 2 and y = 2 (as another
poster pointed out.)  This would probably have led you to the right
conclusion.

__When investigating cases, always look at the simplest possible case
__.

Besides simple cases, other cases to investigate are extreme cases such
as x = y = 1 million, and x = y = 1.000000001.

However, it's best to do the simplest case first.

Another tip here is to look for cases where one of the expressions is
not defined because of a zero denominator.  Here the search is empty
because none of the zero-denom cases: x = 0, y = 0, x = -y can arise.

But, if they could arise, you would have not_enough_info as your
correct answer, arrived at quickly.

Often (but not here), not_enough_info can be shown to be the right
answer by finding a zero denom.

Usually, in this comparison section, there is exactly one question
where not_enough_info is correct.  Although 2 would not be all that
surprising.

If you _never_ say not_enough_info, or if you give that answer >= 3
times, I would suspect your answers.

Paul Epstein


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