The sum of the lengths of two pieces of rope is 65 feet. How long is the shorter piece?

[Gmat_mission]

The sum of the lengths of two pieces of rope is 65 feet. How long is the shorter piece?

(1) The lengths of the pieces of rope are in the ratio 8:5.
(2) One piece of rope is 15 feet longer than the other piece.

[spoiler]OA=D[/spoiler]

Source: GMAT Prep

[deloitte247]

Given that: x + y = 65 feet

Target question => How long is the shorter price?

Statement 1 =>The length of the pieces of rope are 8:5
$$x+y=65............eqn1$$
$$x:y=8:5$$
$$\frac{x}{y}=\frac{8}{5}$$
$$5x=8y\ and\ x=\frac{8y}{5}$$
$$Substitute\ x\ in\ eqn\ 1$$
$$x+y=65\ \ \ \ \ where\ x=\frac{8y}{5}$$
$$\frac{8y}{5}+y=65$$
$$\frac{8y+5y}{5}=65$$
$$\frac{13y}{13}=\frac{65\cdot5}{13}$$
$$y=25\ feet$$
$$Therefore,\ x+25=65$$
$$x=65-25=40\ feet;\ shorter\ piece\ =\ y=25ft$$
$$Statement\ 1\ is\ SUFFICIENT$$

Statement 2 => One piece is 15feet longer than the other piece
i.e x + y = 65; where x = y + 15
$$Therefore,\ y+15+y=65$$
$$\frac{2y}{2}=\frac{65-15}{2}$$
$$y=\frac{50}{2}=25\ feet$$
$$x+25=65$$
$$x=65-25=40\ feet$$
$$shorter\ piece\ =\ y=25\ feet$$
$$Statement\ 2\ is\ SUFFICIENT$$

Since each statement alone is SUFFICIENT,
Answer = D