The largest integer for which (n-1)/n is less than 0.8 is 4 (3/4 = 0.75)

The smallest integer that respect the condition (n-1)/n > 0 is instead 2 (1/2 = 0.5)

Hence, we have to multiply 3/4 * 2/3 * 1/2 = 0.25 > 0.1

The answer is A.

S will have fractions less that 0.8, does not mean all values less than 0.8!
Why just 0.1 x 0.2 x ....... x 0.7, we could also have 0.01 x 0.02 x 0.03 x ..... x 0.77 x 0.78 x 0.79 ???

These fractions are less than 0.8 but n must be an integers too!
So, S can only have {1/2, 2/3, 3/4} ........... [using (n-1) / n ]

Col. A = 1/2 x 2/3 x 3/4 = 1/4 = 0.25
Col. B = 0.1

Hence, option A

Why not the answer is D?

If we take n=1 , it gives us a fraction as 0/1 . so the product of all the fractions wouldn't be zero? isn't 0/1 a positive fraction?

\(\frac{0}{1}\) will yield 0 which is a neutral integer.
0 is neither positive nor negative.

\(\frac{n-1}{n} < 0.8\)

\(1 - \frac{1}{n} < 1 - 0.2\)

\(-\frac{1}{n} < -0.2\)

\(\frac{-1}{n} < \frac{-1}{5}\)

\(\frac{1}{n} > \frac{1}{5}\)

\(n < 5\)

Since set S has positive fractions, by a little math you can tell that \(n>1\), \(\frac{1 - 1}{1} = 0\)

Therefore, \(1 < n < 5\)

Product of all elements of S = \(\frac{2-1}{2}*\frac{3-1}{3}*\frac{4-1}{4} = \frac{1}{2}*\frac{2}{3}*\frac{3}{4} = \frac{1}{4}\) = 0.25 > 0.1

Hence answer is A