D it is yes
A standart deviation never changes when a constant is added to all elements of a same set
The construction of the standart deviation is made on the idea that we observe how far the data are from the average. Thus, the distance will always remain the same if we add a constant to every data present in the set.
To make an analogy, we can imagine an spacecraft. All dimensions of it remain the same no matter where we are. The height and the width will be exactly the same if we are at 100 km from the surface of the earth or at 2 000 km from it. The position of its center of gravity will change compared between the 2 distance (it's the average) but all parts of it will keep the same distance to its center of gravity (similarly to the standart deviation).