1. two integral solutions for 0 < x < 50
2. no integral solutions for 10 < y < 20
3. an integral solution for 100 < x < 200
4. no integral solutions for y < 0
As HCF(11, 67) = 1, so there exists infinite integral solutions for the equation 11x + 67y = 133.
Further, values of x will vary at a difference of 67 and that y will vary at a difference of 11.
Now checking options: 1 is not possible to have two values of x in a span of only 48 terms.
2 may be possible, need to be checked.
3 is certainly true as among 99 consecutive natural numbers we will certainly have a solution for x as from every 67 consecutive numbers there has to be one solution.
4 is clearly not true. (3)