Answer:
Y = Stress / Strain = (F / A) / (l / L) where l is the change in length
Since L is doubled and A remains the same one would expect l, the change in length to also double so Y remains the same.
As an example think of hanging a weight from a spring and the same weight from a similar spring of twice the length - one would expect the longer spring to show twice the extension of the shorter spring.
