The ratio of cats to dogs = 5:11
Target question=> What was the ratio of cats to dogs at the end of the day Tuesday?
Statement 1: No cats were adopted on Tuesday
No information was provided on the number of adopted dogs. Hence, the target question cannot be answered. Thus, statement 1 is NOT SUFFICIENT.

Statement 2: 4 dogs were adopted on Tuesday.
No information was provided on the number of adopted days. Hence, the target question cannot be evaluated. Statement 2 is also NOT SUFFICIENT.

Combining both statements together:
Let the total number of animals at the beginning of Tuesday = x
The ratio of cats to dogs =5x:11x
From statement 1: 0 cat was adopted on Tuesday
From statement 2: 4 dogs were adopted on Tuesday
The ratio of cats to dogs at the end of Tuesday =>
$$\frac{cats}{dogs}=\frac{5x-0}{11x-4}=\frac{5x}{11x-4}$$
Cats : dogs = (5x) : (11x-4)
The value of x is unknown. Hence, the target question cannot be evaluated and both statements combined together are NOT SUFFICIENT.

Answer = option E