sanju09 wrote:ajith wrote:sanju09 wrote:It's sad to see you lost the fifth choice on this occasion, but let's see what's in store
One thing is here to mention before we go for the elucidation, that on GMAT, whenever we find the phrases like x ≠0, ±1, etc, we should make sure that we're going to deal with some rational expression(s) that could contain factors like (x - 0), (x ± 1), etc in its denominators. In order to steer clear of an indeterminate state, they already make us observant with the precincts like that.
From the distance, it could be easily seen that the given rational expression has x^1/2009 as a common factor in the numerator with (x^2 - 1) to spare, and that it has x^1/2010 as a common factor in the denominator, once again with (x^2 - 1) to spare. Hence, (x^2 - 1) is the most visible common factor in the given rational expression, canceled and we are left with x^1/2009/ x^1/2010 = x (x^1/2010)/ x^1/2010 = [spoiler]x[/spoiler].
[spoiler]A[/spoiler]
I do not see it that way Sanju
[x^1/2007 - x^1/2009] if we take x^1/2009 as the common factor
x^1/2009 [x^(1/2007-1/2009) -1) which is
NOT equal to x^1/2009 (x^2 -1)
Similar is the case with denominator
on top of that x^1/2009/x^1/2010
is not equal to x
Oh really! Let each of us give it
another and
closer look, see you soon,
ajith
Sorry cronies for reappearing so late, thanks to a lingering server problem in this part of land since then. Two things to submit, first is that my distance vision didn't work well on this occasion and resulted in assuming rope in a snake sort of thing for me, that's why I suggested my/our self to have a closer look now. I knew the folly in my elucidation through ajith, so I started trying it again on paper. Secondly, I didn't find it to be a correct problem, as long as the choices are concerned. Just useless to say that it's NOT a GMAT query. Following are few efforts made by me, but to no avail:
Multiplying numerator and denominator by x^2010, we get
[x^ (2010/2007) - x^ (2010/2009)]
[x^ (2010/2008) - x^ (2010/2010)]
=
[x^ (1 + 3/2007) - x^ (1 + 1/2009)]
[x^ (1 + 2/2008) - x]
=
x [x^ (3/2007) - x^ (1/2009)]
x [x^ (2/2008) - 1]
And then a weak assumption ([spoiler]
following words are not to be taken as valid[/spoiler])
Owing to the fact that the roots of the order of 2000 applied to a non-zero, non-unity number, x, is so small to assume that we can safely assume
That x^1/2007 = x^1/2008 = x^1/2009 = t, where t tends to 0, but it's never 0 either way.
Hence,
[x^ (1/2007)]^3 - [x^ (1/2009)]
[x^ (1/2008)]^2 - 1
=
t^3 - t
t^2 - 1
=
t(t^2 - 1 )
t^2 - 1
= t
???????????????????
There were few more efforts made by me, but I don't feel like typing so much for nothing. If Anchit is sure that the question is correct from all corners, and also, if he can provide us the source, then I can try it beyond GMAT specifications before saying died.
