rinkumaa4 wrote:
let simplify the equation
2rs>r+s
rs-r>s-rs
r(s-1)>s(1-r)
r/s<(r-1)/(s-1)
stat-1
if r=3 and s=4 .... not true
but if r= 99 and s=2 ..... true
So can some one expain how the statement one itself sufficient.
Error detection will be appriciated on my expaination.......
Hi
The problem that when you did as follows:
2rs>r+s
rs-r>s-rs
r(s-1)>s(1-r)
r(s-1)> -s(r-1)
Is r/s >
-(r-1)/(s-1)??......When you changed the sign '<' you did not put the negative sign in next side
-r/s<(r-1)/(s-1)
Let take your examples again:
r=3 and s=4... -3/4 < 2/3....Yes
r= 99 and s=2... -99/2 < 98....Yes
In both cases left is negative side while right side is positive. So it is Sufficient
You could have stopped at the following step
r(s-1)>s(1-r)..........Based on Statement 1, the right will be always negative and right is positive..........Always Yes.
In same way, we can prove statement 2 is insufficient through following examples.
No need to duplicate work .Any example of the above will lead to yes.
Let s=1/2 & r =100
here if 0<S<1........the left side will always negative while the right side will be always positive...Answer is No.
I hope it helps.