Super tricky question!!

Let's just test a specific case, which meets the given condition that \(n<m<k\).

Let's say \(n = 2\), \(m = 4\) and \(k = 5\)

Plug these values into get: \(\frac{2^{2+4} \times 3^{4+5} \times 5^{2+5}}{10^x}\)

Simplify: \(\frac{2^{6} \times 3^{9} \times 5^{7}}{10^x}\)

Rearrange to get: \(\frac{2^{6} \times 5^{6} \times 5^{1} \times 3^{9} }{10^x}\)

Combine the first two terms of the numerator to get: \(\frac{10^{6} \times 5^{1} \times 3^{9} }{10^x}\)

Rewrite as follows: \((5^{1} \times 3^{9})\frac{10^{6}}{10^x}\)

So, in order for the original expression to be an integer, the maximum possible value of x is 6.

When we plug \(n = 2\), \(m = 4\) and \(k = 5\) into the five answer choices, only C (\(n + m\)) evaluates to equal 6

Answer: C