Walkabout wrote:
\frac{0.99999999}{1.0001}-\frac{0.99999991}{1.0003}=
(A) 10^(-8)
(B) 3*10^(-8)
(C) 3*10^(-4)
(D) 2*10^(-4)
(E) 10^(-4)
(A) 10^(-8)
(B) 3*10^(-8)
(C) 3*10^(-4)
(D) 2*10^(-4)
(E) 10^(-4)
The best solution is already outlined by Bunuel/Karishma. Because this is an Official Problem, I was sure there might be another way to do this.
So i did spend some time and realized that 0.99999999 might be a multiple of 1.0001 because of the non-messy options and found this :
9*1.0001 = 9.0009 ; 99*1.0001 = 99.0099 and as because the problem had 9 eight times, we have 9999*1.0001 = 9999.9999.
Again, looking for a similar pattern, the last digit of 0.99999991 gave a hint that maybe we have to multiply by something ending in 7, as because we have 1.0003 in the denominator. And indeed 9997*1.0001 = 9999.9991. Thus, the problem boiled down to 9999*10^{-4} - 9997*10^{-4} = 2*10^{-4}
D.
Maybe a bit of luck was handy.