The number of newly detected instances possible when set to .85 multiplied by the previous number number of detected instances must create an integer x when divided by .85.

Let x= the previous number of detected instances.

A.) .85*x=1
x doesn't equal an integer so no.

B.) .85*x= 5. No

C.) .85*x= 11. No

D.) .85*x=15. No.

E.) .85*x=17. Yes, x=20.

E is our answer.

Number of cases infected must be an integer ( assuming that we can divide the cases only in to two parts , those who have got it and those who have not got it )

So it must be a multiple of 0.85 , hence the answer is 17