joyseychow wrote:

If x and y are positive integers and x/y has a remainder of 5, what is the smallest possible value of xy?

This ques is from Man prep book. I don't understand why smallest value of x is 5 and not 11.

This is a classic trap: 0 is a multiple of every natural number. 5 can be written as (0*6)+5 which also means that when 5 is divided by 6, remainder is 5.

In order to find the minimum possible value of xy, we will try to make both x and y the smallest. To leave a remainder of 5, minimum possible value of y will be 6. Smallest possible number that will result in the remainder of 5 is then 5 (as explained above). So, xy=5*6=30

Hope it helps