GMAT Prep

bubbliiiiiiii wrote:

1/p>r/r^2+2;

1) p=r;
we have 1/r> r/r^2+2;

now consider r=-3 we have; 1/r =-1/3

and r/r^2+2=-3/11; now -1/3<-3/11; i.e. inequality 1/p>r/r^2+2 doesn't hold true;

now consider r=3; we have; 1/r= 1/3;
and r/r^2+2=3/11, now 1/3>3/11; i.e. inequality 1/p>r/r^2+2 holds true;

hence 1 alone is not sufficient to answer the question.

2)
r>0; insufficient as we don't know the relationship between r and p;

combining yes we will consider only positive cases for which answer will always be yes as shown above.

hence C

1/p > r/(r²+2) ?

1) p = r
1/r > r/(r²+2) ?
mutiply by (r²+2) [won't change sign because r² + 2 will always yield + value]
(r²+2)/r > r ?
(r²+2)/r - r > 0 ?
(r²+2-r²)/r > 0 ?
2/r > 0 ? -> Insufficient

2) r > 0
Don't know anything about p and 1/p could be any negative or positive number.

3) Combined:
2/+positive > 0 ? YES!!! Will yield a positive number greater than 0.

Thanks all.