Easy interview question got harder: given numbers 1..100, find the missing number(s) given exactly k are missing

Question

I had an interesting job interview experience a while back. The question started really easy:

Q1: We have a bag containing numbers

Answer 1

Can you check if every number exists? If yes you may try this:

S = sum of all numbers in the bag (S < 5050)
Z = sum of the missing numbers 5050 - S

if the missing numbers are x and y then:

x = Z - y and
max(x) = Z - 1

So you check the range from 1 to max(x) and find the number