How come deeper layer shows faster time of grep?

Hello guys,
I was experimenting with Docker recently, and I came up with a question.
In general, deeper or more the layers are, more overhead occrus is quite simple to undertstand.
However, I created one Dockerfile creating 16 50mb files in one layer and another Dockerfile creating 50mb file in each of 16 layers and built them.
When I used grep command in the container where those files are created, somehow, creating 16 of 50mb files in one layer shows faster grep time. Is it because my implementation of Dockerfile is wrong or… is there any idea you guys can suggest??