Statement(A) : When a body is dropped or thrown horizontally from the same height, it would reach the ground at the same time 

Statement(B) : Horizontal velocity has no effect on the vertical direction

It is true that when a body is dropped or thrown horizontally from same height it will reach the ground in same time. Time of decent depends on height from which is projected it is also 

true that horizontal velocity do not affect the motion of a body in vertical direction