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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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