k is 96% greater than its reciprocal
The reciprocal of k is 1/k
So, we can write: k = (1/k) + (96% of 1/k)
In other words: k = (1/k) + 0.96(1/k)
Simplify: k = 1.96(1/k)
Simplify: k = 1.96/k
Multiply both sides by k to get: k² = 1.96
Solve: k = 1.4 of k = -1.4
Rewrite as follows: k = 7/5 of k = -7/5

ASIDE: Although it doesn't change the outcome, we can ELIMINATE the solution k = -7/5
Here's why:
If k = -7/5 then 1/k = -5/7
The question tells us that "k is 96% greater than 1/k, but we can see that k is actually less than 1/k (that is: -7/5 < -5/7)
So, k CANNOT equal -7/5

So, it MUST be the case that k = 7/5


Which of the following is an integer?
If k = 7/5, we can see that answer choice C must be an integer.

C) $\frac{5k}{7}=(k)(\frac{5}{7})=(\frac{7}{5})(\frac{5}{7})=\frac{35}{35}=1$

Answer: C

Cheers,
Brent