I believe that this is part of a larger question that goes as follows:

If k is an integer, what is the value of k?

1/5 < 1/(k-1) < 1/2

If 1/something is greater than 1/5 and less than 1/2 what are some values for something?

Well, we know that 1/5 < 1/4 < 1/2, and we know that 1/5 < 1/3 < 1/2

Since something is an integer, it looks like 3 and 4 are the only possible values of something.

Since we're using something as a placeholder for (k - 1), we can conclude that:
(k - 1) = 3 or (k - 1) = 4
Solve to get: k = 4 or k = 5

Aside: I call the above technique the "Something Method." If anyone is interested, we have a free video on this topic: https://www.gmatprepnow.com/module/gmat- ... ing?id=988

Cheers,
Brent

kamalakarthi wrote:
1/5 < 1/(k-1) < 1/2

If we don't restrict k to integer values, we can solve the above as follows:

First examine this part: 1/5 < 1/(k-1)
From this, we can conclude that (k - 1) < 5
Solve to get: k < 6

Then examine this part: 1/(k-1) < 1/2
From this, we can conclude that (k - 1) > 2
Solve to get: k > 3

Combine to get: 3 < k < 6

Cheers,
Brent